MATH 225N Week 8 Final Exam questions and solutions

Document Content and Description Below

MATH 225N Week 8 Final Exam Question 1 1/1 points A fitness center claims that the mean amount of time that a person spends at the gym per visit is 33 minutes. Identify the null hypothesis, H0, a... nd the alternative hypothesis, Ha, in terms of the parameter μ. That is correct! H0: μ≠33; Ha: μ=33 H0: μ=33; Ha: μ≠33 H0: μ≥33; Ha: μ<33 H0: μ≤33; Ha: μ>33 Answer Explanation Correct answer: H0: μ=33; Ha: μ≠33 Let the parameter μ be used to represent the mean. The null hypothesis is always stated with some form of equality: equal (=), greater than or equal to (≥), or less than or equal to (≤). Therefore, in this case, the null hypothesis H0 is μ=33. The alternative hypothesis is contradictory to the null hypothesis, so Ha is μ≠33. Question 2 1/1 points The answer choices below represent different hypothesis tests. Which of the choices are righttailed tests? Select all correct answers. That is correct! H0:X≥17.1, Ha:X<17.1   H0:X=14.4, Ha:X≠14.4   H0:X≤3.8, Ha:X>3.8   H0:X≤7.4, Ha:X>7.4   H0:X=3.3, Ha:X≠3.3  Answer Explanation Correct answer: H0:X≤3.8, Ha:X>3.8 H0:X≤7.4, Ha:X>7.4Remember the forms of the hypothesis tests.  Right-tailed: H0:X≤X0, Ha:X>X0.  Left-tailed: H0:X≥X0, Ha:X<X0.  Two-tailed: H0:X=X0, Ha:X≠X0. So in this case, the right-tailed tests are:  H0:X≤7.4, Ha:X>7.4  H0:X≤3.8, Ha:X>3.8 Question 3 1/1 points Find the Type II error given that the null hypothesis, H0, is: a building inspector claims that no more than 15% of structures in the county were built without permits. That is correct! The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, no more than 15% of the structures really were built without permits. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures really were built without permits. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, at most 15% of the structures were built without permits. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits. Answer Explanation Correct answer: The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits. A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is when the building inspector thinks that no more than 15% of the structures were built without permits when, in fact, more than 15% of the structures were built without permits.    Question 4 1/1 points Suppose a chef claims that her meatball weight is less than 4 ounces, on average. Several of her customers do not believe her, so the chef decides to do a hypothesis test, at a 10% significance level, to persuade them. She cooks 14 meatballs. The mean weight of the sample meatballs is 3.7 ounces. The chef knows from experience that the standard deviation for her meatball weight is 0.5 ounces.  H0: μ≥4; Ha: μ<4  α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? That is correct! Test statistic = minus 2 point 2 4$$ Test statistic = minus 2 point 2 4 - correct Answer Explanation Correct answers:  Test statistic = minus 2 point 2 4 $\text{Test statistic = }-2.24$ The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean weight, x¯=3.7. The sample the chef uses is 14 meatballs, so n=14. She knows the standard deviation of the meatballs, σ=0.5. Lastly, the chef is comparing the population mean weight to 4 ounces. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the test statistic: z0=x¯−μ0σn√=3.7−40.514√≈−0.30.134≈−2.24 So, the test statistic for this hypothesis test is z0=−2.24.     Question 5 1/1 points What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=1.74? (Do not round your answer; compute your answer using a value from the table below.) z1.51.61.71.81.90.000.9330.9450.9550.9640.9710.010.9340.9460.9560.9650.9720.020.9360.947 0.9570.9660.9730.030.9370.9480.9580.9660.9730.040.9380.9490.9590.9670.9740.050.9390.951 0.9600.9680.9740.060.9410.9520.9610.9690.9750.070.9420.9530.9620.9690.9760.080.9430.954 0.9620.9700.9760.090.9440.9540.9630.9710.977 That is correct! 0 point 0 4 1$$ 0 point 0 4 1 - correct Answer Explanation Correct answers:  0 point 0 4 1 $0.041$  The p-value is the probability of an observed value of z=1.74 or greater if the null hypothesis is true, because this hypothesis test is right-tailed. This probability is equal to the area under the Standard Normal curve to the right of z=1.74.A standard normal curve with two points labeled on the horizontal axis. The mean is labeled at 0.00 and an observed value of 1.74 is labeled. The area under the curve and to the right of the observed value is shaded. Using the Standard Normal Table, we can see that the p-value is equal to 0.959, which is the area to the left of z=1.74. (Standard Normal Tables give areas to the left.) So, the p-value we're looking for is p=1−0.959=0.041. Question 6 1/1 points Kenneth, a competitor in cup stacking, claims that his average stacking time is 8.2 seconds. During a practice session, Kenneth has a sample stacking time mean of 7.8 seconds based on 11 trials. At the 4% significance level, does the data provide sufficient evidence to conclude that Kenneth's mean stacking time is less than 8.2 seconds? Accept or reject the hypothesis given the sample data below.  H0:μ=8.2 seconds; Ha:μ<8.2 seconds  α=0.04 (significance level)  z0=−1.75  p=0.0401 That is correct!Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. Reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. Reject the null hypothesis because the value of z is negative. Reject the null hypothesis because |−1.75|>0.04. Do not reject the null hypothesis because |−1.75|>0.04. Answer Explanation Correct answer: Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. In making the decision to reject or not reject H0, if α>p-value, reject H0 because the results of the sample data are significant. There is sufficient evidence to conclude that H0 is an incorrect belief and that the alternative hypothesis, Ha, may be correct. If α≤p-value, do not reject H0. The results of the sample data are not significant, so there is not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct. In this case, α=0.04 is less than or equal to p=0.0401, so the decision is to not reject the null hypothesis.    QUESTION 7 1/1 POINTS A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test? That is correct!{H0:p=0.81Ha:p>0.81 {H0:p≠0.81Ha:p=0.81 {H0:p=0.81Ha:p<0.81 {H0:p=0.81Ha:p≠0.81 Answer Explanation Correct answer: {H0:p=0.81Ha:p≠0.81 First verify whether all of the conditions have been met. Let p be the population proportion for the senior citizen patients treated at Amelia's hospital who take at least one prescription medication. 1. Since there are two independent outcomes for each trial, the proportion follows a binomial model. 2. The question states that the sample was collected randomly. 3. The expected number of successes, np=47.79, and the expected number of failures, nq=n(1−p)=11.21, are both greater than or equal to 5. Since Amelia is testing whether the proportion is the same, the null hypothesis is that p is equal to 0.81 and the alternative hypothesis is that p is not equal to 0.81. The null and alternative hypotheses are shown below. {H0:p=0.81Ha:p≠0.81 QUESTION 8 1/1 POINTSA researcher claims that the proportion of cars with manual transmission is less than 10%. To test this claim, a survey checked 1000 randomly selected cars. Of those cars, 95 had a manual transmission. The following is the setup for the hypothesis test: {H0:p=0.10Ha:p<0.10 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. That is correct! $$Test_Statistic=−0.53 Answer Explanation Correct answers:  $\text{Test_Statistic}=-0.53$Test_Statistic=−0.53 The proportion of successes is p^=951000=0.095. The test statistic is calculated as follows: z=p^−p0p0⋅(1−p0)n−−−−−−√ z=0.095−0.100.10⋅(1−0.10)1000−−−−−−−−√ z≈−0.53 QUESTION 9 1/1 POINTS A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. . The following is the setup for this hypothesis test: H0:p = 0.12Ha:p ≠ 0.12 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve: z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029 -1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 -1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 -1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 -1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 That is correct! $$P-value=0.124 Answer Explanation Correct answers:  $\text{P-value=}0.124$P-value=0.124 Here are the steps needed to calculate the p-value for a hypothesis test for a proportion:1. Determine if the hypothesis test is left tailed, right tailed, or two tailed. 2. Compute the value of the test statistic. 3. If the hypothesis test is left tailed, the p-value will be the area under the standard normal curve to the left of the test statistic z0 If the test is right tailed, the p-value will be the area under the standard normal curve to the right of the test statistic z0 If the test is two tailed, the p-value will be the area to the left of −|z0| plus the area to the right of |z0| under the standard normal curve For this example, the test is a two tailed test and the test statistic, rounding to two decimal places, is z=0.1033−0.120.12(1−0.12)900−−−−−−−−−−−−√≈−1.54. Thus the p-value is the area under the Standard Normal curve to the left of a z-score of -1.54, plus the area under the Standard Normal curve to the right of a z-score of 1.54. z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029 -1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 -1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 -1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 -1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 From a lookup table of the area under the Standard Normal curve, the corresponding area is then 2(0.062) = 0.124. QUESTION 10 1/1 POINTSAn economist claims that the proportion of people who plan to purchase a fully electric vehicle as their next car is greater than 65%. To test this claim, a random sample of 750 people are asked if they plan to purchase a fully electric vehicle as their next car Of these 750 people, 513 indicate that they do plan to purchase an electric vehicle. The following is the setup for this hypothesis test: H0:p=0.65 Ha:p>0.65 In this example, the p-value was determined to be 0.026. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%.) That is correct! The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim. Answer Explanation Correct answer: The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. To come to a conclusion and interpret the results for a hypothesis test for proportion using the PValue Approach, the first step is to compare the p-value from the sample data with the level of significance.The decision criteria is then as follows: If the p-value is less than or equal to the given significance level, then the null hypothesis should be rejected. So, if p≤α, reject H0; otherwise fail to reject H0. When we have made a decision about the null hypothesis, it is important to write a thoughtful conclusion about the hypotheses in terms of the given problem's scenario. Assuming the claim is the null hypothesis, the conclusion is then one of the following:  if the decision is to reject the null hypothesis, then the conclusion is that there is enough evidence to reject the claim.  if the decision is to fail to reject the null hypothesis, then the conclusion is that there is not enough evidence to reject the claim. Assuming the claim is the alternative hypothesis, the conclusion is then one of the following:  if the decision is to reject the null hypothesis, then the conclusion is that there is enough evidence to support the claim.  if the decision is to fail to reject the null hypothesis, then the conclusion is that there is not enough evidence to support the claim. In this example, the p-value = 0.026. We then compare the p-value to the level of significance to come to a conclusion for the hypothesis test. In this example, the p-value is less than the level of significance which is 0.05. Since the p-value is greater than the level of significance, the conclusion is to reject the null hypothesis. QUESTION 11 1/1 POINTS Becky's statistics teacher was teaching the class how to perform the z-test for a proportion. Becky was bored because she had already mastered the test, so she decided to see if the coin she had in her pocket would come up heads or tails in a truly random fashion when flipped. She discretely flipped the coin 30 times and got heads 18 times. Becky conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of heads is different from 50%.Which answer choice shows the correct null and alternative hypotheses for this test? That is correct! H0:p=0.6; Ha:p>0.6, which is a right-tailed test. H0:p=0.5; Ha:p<0.5, which is a left-tailed test. H0:p=0.6; Ha:p≠0.6, which is a two-tailed test. H0:p=0.5; Ha:p≠0.5, which is a two-tailed test. Answer Explanation Correct answer: H0:p=0.5; Ha:p≠0.5, which is a two-tailed test. The null hypothesis should be true proportion: H0:p=0.5. Becky wants to know if the true proportion of heads is different from 0.5. This means that we just want to test if the proportion is not 0.5. So, the alternative hypothesis is Ha:p≠0.5, which is a two-tailed test. QUESTION 12 1/1 POINTS John owns a computer repair service. For each computer, he charges $50 plus $45 per hour of work. A linear equation that expresses the total amount of money John earns per computer is y=50+45x. What are the independent and dependent variables? What is the y-intercept and the slope? That is correct! The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer. John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45. The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer. John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50. The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer. John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45. The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer. John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50.Answer Explanation Correct answer: The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer. John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45. The independent variable (x) is the amount of time John fixes a computer because it is the value that changes. He may work different amounts per computer, and his earnings are dependent on how many hours he works. This is why the amount, in dollars, John earns for a computer is the dependent variable (y). The y-intercept is 50 (b=50). This is his one-time fee. The slope is 45 (a=45). This is the increase for each hour he works. QUESTION 13 1/1 POINTS Ariana keeps track of the amount of time she studies and the score she gets on her quizzes. The data are shown in the table below. Which of the scatter plots below accurately records the data? Hours studying Quiz score 1 5 2 5 3 7 4 9 5 9That is correct! A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 10 in increments of 2. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right-parentheses; leftparenthesis 3 comma 7 right-parentheses; left-parenthesis 4 comma 9 right-parentheses; leftparenthesis 5 comma 9 right-parentheses. All values are approximate.A scatterplot has a horizontal axis labeled Hours studying from 0 to 10 in increments of 2 and a vertical axis labeled Quiz score from 0 to 6 in increments of 1. The following points are plotted: left-parenthesis 5 comma 1 right-parentheses; left-parenthesis 5 comma 2 right-parentheses; leftparenthesis 7 comma 3 right-parentheses; left-parenthesis 9 comma 4 right-parentheses; leftparenthesis 9 comma 5 right-parentheses. All values are approximate.A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 9 in increments of 1. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right-parentheses; leftparenthesis 3 comma 7 right-parentheses; left-parenthesis 4 comma 8 right-parentheses; leftparenthesis 5 comma 8 right-parentheses.A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 12 in increments of 2. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right-parentheses; leftparenthesis 3 comma 8 right-parentheses; left-parenthesis 4 comma 8 right-parentheses; leftparenthesis 5 comma 11 right-parentheses. All values are approximate. Answer Explanation Correct answer:A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 10 in increments of 2. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right-parentheses; leftparenthesis 3 comma 7 right-parentheses; left-parenthesis 4 comma 9 right-parentheses; leftparenthesis 5 comma 9 right-parentheses. All values are approximate. The values for hours studying correspond to x-values, and the values for quiz score correspond to y-values. Each row of the table of data corresponds to a point (x,y) plotted in the scatter plot. For example, the first row, 1,5, corresponds to the point (1,5). Doing this for every row in the table, we find the scatter plot should have points (1,5), (2,5), (3,7), (4,9), and (5,9). QUESTION 14 1/1 POINTS Data is collected on the relationship between time spent playing video games and time spent with family. The data is shown in the table and the line of best fit for the data is y^=−0.27x+57.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables. Video Games (Minutes) 306090120 Time with Family (Minutes) 50403525 According to the line of best fit, the predicted number of minutes spent with family for someone who spent 95 minutes playing video games is 31.85. Is it reasonable to use this line of best fit to make the above prediction?That is correct! The estimate, a predicted time of 31.85 minutes, is unreliable but reasonable. The estimate, a predicted time of 31.85 minutes, is both unreliable and unreasonable. The estimate, a predicted time of 31.85 minutes, is both reliable and reasonable. The estimate, a predicted time of 31.85 minutes, is reliable but unreasonable. Answer Explanation Correct answer: The estimate, a predicted time of 31.85 minutes, is both reliable and reasonable. The data in the table only includes video game times between 30 and 120 minutes, so the line of best fit gives reasonable predictions for values of x between 30 and 120. Since 95 is between these values, the estimate is both reliable and reasonable. QUESTION 15 0/1 POINTS Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015? Select all that apply.That's not right.  yˆ=38,000+2500x   yˆ=38,000−3500x   yˆ=−38,000+2500x   yˆ=38,000−1500x  Answer Explanation Correct answer: yˆ=38,000+2500x yˆ=38,000−1500x Population change can be positive or negative, and it can increase or decrease. Based on the given information, there are no practical limits to population change, although there are limits such as the decrease in population cannot exceed the current population (as it would leave a negative number of people in the country), or the increase in population could be limited by other real-world factors (such as lack of space or legal immigration limits). Your answer: yˆ=38,000+2500x QUESTION 17 1/1 POINTS An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the color index, or B−V index, and distance (in light years) from Earth for 30 stars. The color index of a star is the difference in the light absorption measured from the star using two different light filters (a B and a V filter). This then allows the scientist to know the star's temperature and a negative value means a hot blue star. A light year is the distance light can travel in 1 year, which is approximately 5.9 trillion miles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places. B-V index Distance (ly) 1.1 1380 0.4 556 1.0 771 0.5 304 1.4 5321.0 751 0.5 267 0.8 229 0.5 552 HelpCopy to ClipboardDownload CSV That is correct! $$r= 0.18 Answer Explanation Correct answers:  $\text{r= }0.18$r= 0.18 The correlation coefficient can be calculated easily with Excel using the built-in CORREL function. 1. Open the accompanying data set in Excel. 2. In an open cell, type "=CORREL(A2:A31,B2:B31)", and then hit ENTER. You could label the result of this cell by writing "Correlation coefficient" or "r" in an adjacent open cell. The correlation coefficient, rounded to two decimal places, is r≈0.18. QUESTION 18 0/1 POINTSThe weight of a car can influence the mileage that the car can obtain. A random sample of 20 cars’ weights and mileage is collected. The table for the weight and mileage of the cars is given below. Use Excel to find the best fit linear regression equation, where weight is the explanatory variable. Round the slope and intercept to three decimal places. Weight Mileage 30.0 32.2 20.0 56.0 20.0 46.2 45.0 19.5 40.0 23.6 45.0 16.7 25.0 42.2 55.0 13.2 17.5 65.4 HelpCopy to ClipboardDownload CSVThat's not right. y = $$1.181 x + $$71.374 Answer Explanation y = 1$$ x + 2$$ Correct answers:  1$-1.181$−1.181  2$71.374$71.374 To find the best fit for the given data, use Excel. 1. Open Excel. Enter the values of weight in column A and mileage in column B. Highlight all the cells containing the data. 2. From the Insert tab, select Scatter. Use Scatter with only Markers, the first type of scatter chart. A simple plot is shown. 3. To add the linear fit to the graph, click anywhere inside the graph area. Select the Layout tab from the Chart Tools. Click on the Trendline icon and select the Linear Trendline option. The line of best fit is added to the graph. 4. For the equation of the line of best fit, click on Trendline and select More Trendline Options.... 5. Check the Display Equation on chart box. The equation of line of best fit is shown on the graph. 6. To change the number of decimal places in the trendline equation, right-click on the equation for the trendline and select Format Trendline Label.... 7. Select Number under Category, change the number of decimal places to 3, and click Close. Thus, the equation of line of best fit with slope and intercept rounded to three decimal places is yˆ=−1.181x+71.374. QUESTION 19 1/1 POINTSA farmer divided his piece of land into 4 equivalent groups. The quality of the soil is the same across the 4 groups of land. He planted the same crop in all 4 groups of land and recorded the yield of the crop in all 4 groups for a 4 week period. Is the study observational or experimental? If it is an experiment, what is the controlled factor? That is correct! The study is an observational study. The study is an experiment. The controlled factor is the 4 week observation period. The study is an experiment. The controlled factor is the land. The study is an experiment. The controlled factor is the growth of the crops. Answer Explanation Correct answer: The study is an observational study. The samples are chosen using an appropriate process; however, no attempt is made to control any aspect of the sample even though the variables of interest are recorded for each group. QUESTION 20 1/1 POINTSTo test the effectiveness of a drug proposed to relieve symptoms of headache, physicians included participants for a study. They gave the drug to one group and a drug with no therapeutic effect to another group. Which group receives the placebo? That is correct! the physicians the group that received the drug for headache the group that received the drug with no therapeutic effect all of the people in the study Answer Explanation Correct answer: the group that received the drug with no therapeutic effect When the experimental units are people, applying treatments that should be inert can actually have effects. In this study, the drug with no therapeutic effects is the placebo, so the group that receives that drug receives the placebo. QUESTION 21 1/1 POINTSA doctor notes her patient's temperature in degrees Fahrenheit every hour to make sure the patient does not get a fever. What is the level of measurement of the data? That is correct! nominal ordinal interval ratio Answer Explanation Correct answer: interval This is interval data because degrees Fahrenheit is a numerical scale where differences are meaningful. However, because Fahrenheit does not have a true zero value, it is not ratio data. QUESTION 22 0/1 POINTS As a member of a marketing team, you have been tasked with determining the number of DVDs that people have rented over the past six months. You sample twenty adults and decide that the best display of data is a frequency table for grouped data. Construct this table using four classes.15,31,28,19,14,18,28,19,10,19,10,24,14,18,24,27,10,18,16,23 That's not right. Lower Class Limit Upper Class Limit Frequency $$10 $$15 $$6 $$16 $$21 $$7 $$22 $$27 $$4 $$18 $$33 $$3 Answer ExplanationLower Class Limit Upper Class Limit Frequency 1$$ 2$$ 3$$ 4$$ 5$$ 6$$ 7$$ 8$$ 9$$ 10$$ 11$$ 12$$ Correct answers:  1$10$10  2$15$15  3$6$6  4$16$16  5$21$21  6$7$7  7$22$22  8$27$27  9$4$4  10$28$28  11$33$33  12$3$3 Note that the data is not ordered and that we have been asked to use 4 classes. To determine the class width, use the formula: Max Value−Min ValueNumber of Classes=31−104=5.25. Since this value is not an integer, round to 6.Use the minimum value, 10, for the lower class limit of the first class. To find all other lower class limits, add the class width, 6. For example, the second lower class limit would be: 10+6=16. Lower Class Limit Upper Class Limit Frequency 10 16 22 28 To find the upper class limits, add the class width minus 1, to each lower class limit. For example, the upper class limit of the first class would be: 10+5=15. Lower Class Limit Upper Class Limit Frequency 10 15 16 21 22 27 28 33To find the frequency for each class, count the number of data values that fall within the range of each class. For example, the data values 15, 14, 10, 10, 14, and 10 fall within the range of the first class, 10-15. So, the frequency of this class is 6. Lower Class Limit Upper Class Limit Frequency 10 15 6 16 21 7 22 27 4 28 33 3 QUESTION 23 1/1 POINTS The histogram below displays the weights of rainbow trout (in pounds) caught by all visitors at a lake on a Saturday afternoon. According to this histogram, which range of weights (in pounds) contains the lowest frequency?A histogram has a vertical axis labeled Frequency and has a horizontal axis that measures six categories of rainbow trout weight (in pounds). Reading from left-to-right, the weight and frequency of each category are: 4.5 to 6.5 has frequency of 4, 6.5 to 8.5 has frequency 5, 8.5 to 10.5 has frequency 7, 10.5 to 12.5 has frequency 3, 12.5 to 14.5 has frequency 1, 14.5 to 16.5 has frequency 2. That is correct! $$greater than 12.5 but less than 14.5 Answer Explanation Correct answers: $\text{greater than }12.5\ \text{but less than }14.5$greater than 12.5 but less than 14.5 The range 12.5−14.5 has the lowest bar in the histogram, which means that this range of values also has the lowest frequency. Therefore, 1 visitor caught a rainbow trout that weighed greater than 12.5 but less than 14.5 pounds. QUESTION 24 1/1 POINTS Describe the shape of the given histogram. A histogram has a horizontal axis from 0 to 16 in increments of 2 and a vertical axis labeled Frequency from 0 to 10 in increments of 2. The histogram contains vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the frequency is listed second: 0, 0; 1, 0; 2, 6; 3, 6; 4, 7; 5, 6; 6, 6; 7, 6; 8, 7; 9, 6; 10, 6; 11, 6; 12, 6; 13, 7; 14, 0; 15, 0. That is correct! uniform unimodal and symmetricunimodal and left-skewed unimodal and right-skewed bimodal Answer Explanation Correct answer: uniform All the bars in a uniform histogram are about the same height. QUESTION 25 1/1 POINTS The bar graph below shows the number of boys and girls in different classes.A bar graph has a horizontal axis labeled Classes and a vertical axis labeled Students from 0 to 16 in increments of 2. There are two vertical bars above each horizontal axis label, with the bar on the left representing Boys and the bar on the right representing Girls. The bars have heights as follows, with the horizontal axis label listed first and the bar heights listed second from left to right: Mrs. Brown, 10 and 15; Ms. James, 11 and 12. How many total students are in Ms. James's class? Do not include the units in your answer. That is correct! $$23 Answer Explanation Correct answers: $23$23 To find the number of students in Ms. James's class, find the heights of the bars for that class and add them. In this case, we find it is 11+12=23. QUESTION 26 0/1 POINTS The line graph shown below represents the number of TVs in a house by square footage (in hundreds of feet). According to the information above, which of the following is an appropriate analysis of square footage and TVs? A line graph has an x-axis labeled Square Footage (in hundreds of feet) in increments of one, and a y-axis labeled Number of TV's in increments of one. Beginning at the point start parentheses 6,2 end parentheses, a line increases to the point start parentheses 8.5,3 end parentheses. The line remains constant to the point start parentheses 10,3 end parentheses. The line then increases, passing through the point start parentheses 12,5 end parentheses and continues increasing until it reaches the point start parentheses 16,6 end parentheses.That's not right. From the data, the number of TVs doubled from a square footage of 8.5 and 10. From the data, there is a steady decrease in the square footage and number of TVs. From the data, there is a steady increase in the square footage and number of TVs. From the data, when the square footage is between 8.5 and 10, the number of TVs remains the same. Answer Explanation Correct answer: From the data, when the square footage is between 8.5 and 10, the number of TVs remains the same. Given the line graph, at a square footage of 8.5, the number of TVs is 3. At a square footage of 10, the number of TVs is also 3. Therefore, when the square footage is between 8.5 and 10, the number of TVs remains the same. Your answer: From the data, there is a steady increase in the square footage and number of TVs. This response is not correct. While most of the line is increasing, the number of TVs remains the same between a square footage of 8.5 and 10.QUESTION 27 1/1 POINTS Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are listed below. 16,14,14,21,15 Find the mean boxes sold. That is correct! $$mean=16 boxes Answer Explanation Correct answers:  $\text{mean=}16\text{ boxes}$mean=16 boxes Remember that the mean is the sum of the numbers divided by the number of numbers. There are 5 numbers in the list. So we find that the mean boxes sold is QUESTION 28 1/1 POINTS Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median. 20,46,19,14,42,26,33 That is correct! $$median=26 thousands of dollars Answer ExplanationCorrect answers:  $\text{median=}26\text{ thousands of dollars}$median=26 thousands of dollars It helps to put the numbers in order. 14,19,20,26,33,42,46 Now, because the list has length 7, which is odd, we know the median number will be the middle number. In other words, we can count to item 4 in the list, which is 26. So the median price (in thousands of dollars) of randomly selected trucks at a car dealership is 26. QUESTION 29 1/1 POINTS Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the following number of cards drawn from a deck until a queen appears. 3,12,3,11,5,5,3,10,12 That is correct! $$mode=3 cards Answer Explanation Correct answers:  $\text{mode=}3\text{ cards}$mode=3 cards If we count the number of times each value appears in the list, we get the following frequency table: Value Frequency 3 3 5 210 1 11 1 12 2 Note that 3 occurs 3 times, which is the greatest frequency, so 3 is the mode of the number of cards drawn from a deck until a queen appears. QUESTION 30 1/1 POINTS Given the following histogram, decide if the data is skewed or symmetrical.A bar graph has a horizontal axis titled Values labeled from 2 to 18 in increments of 2 and a vertical axis titled Frequency labeled from 0 to 200 in increments of 50. 14 bars are plotted, above the numbers 2 to 16. From left to right, the heights of the bars are as follows: 1. 5. 10. 40, 75, 125, 190, 180, 130, 125, 60, 25,20, 10. All values are approximate. That is correct! The data are skewed to the left.The data are skewed to the right. The data are symmetric. Answer Explanation Correct answer: The data are symmetric. Note that the histogram appears to be roughly symmetric. So the data are symmetric. QUESTION 31 1/1 POINTS Which of the data sets represented by the following box and whisker plots has the smallest standard deviation?Four horizontal box-and-whisker plots share a vertical axis with the classes D, C, B, and A and a horizontal axis from 0 to 120 in increments of 20. The box-and-whisker plot above the class label A has the following five-number summary: 44, 69, 77, 82, and 112. The box-and-whisker plot above the class label B has the following five-number summary: 19, 64, 78, 87, and 121. The box-and-whisker plot above the class label C has the following five-number summary: 60, 72, 75, 80, and 92. The box-and-whisker plot above the class label D has the following five-number summary: 2, 63, 77, 92, and 138. All values are approximate. That is correct! AB C D Answer Explanation Correct answer: C Remember that the standard deviation is a measure of how spread out the data is. If the values are concentrated around the mean, then a data set has a lower standard deviation. A box and whisker plot with short whiskers and a short box has values that are less spread out, and hence has a smaller standard deviation. QUESTION 32 1/1 POINTS The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation.A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is short and the most spread out, curve Upper B is tall and the least spread out, and curve C is farther to the left than A. That is correct! A B C Answer Explanation Correct answer:B Remember that the standard deviation tells how spread out the normal distribution is. So a high standard deviation means the graph will be short and spread out. A low standard deviation means the graph will be tall and skinny. The distribution that is the tallest and least spread out is B, so that has the smallest standard deviation. QUESTION 33 1/1 POINTS Brayden tosses a coin 500 times. Of those 500 times, he observes heads a total of 416 times. Calculations show that the probability of this occurring by chance is less than 0.01, assuming the coin is fair. Determine the meaning of the significance level. That is correct! We expect that 416 of every 500 coin tosses will result in heads. At the 0.01 level of significance, the coin is likely not a fair coin. There is certainty that the coin is not a fair coin. The results are not statistically significant at the 0.05 level of significance. Answer ExplanationCorrect answer: At the 0.01 level of significance, the coin is likely not a fair coin. The results of the experiment are significant at the 0.01 level of significance. This means the probability that the outcome was the result of chance is 0.01 or less. Because of this, we can be fairly confident, but not certain, that the coin is not a fair coin. QUESTION 34 1/1 POINTS Is the statement below true or false? Independent is the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs. That is correct! True False Answer Explanation Correct answer: True Independent is defined as the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs. QUESTION 35 1/1 POINTSOf the following pairs of events, which pair has mutually exclusive events? That is correct! rolling a sum greater than 7 from two rolls of a standard die and rolling a 4 for the first throw drawing a 2 and drawing a 4 with replacement from a standard deck of cards rolling a sum of 9 from two rolls of a standard die and rolling a 2 for the first roll drawing a red card and then drawing a black card with replacement from a standard deck of cards Answer Explanation Correct answer: rolling a sum of 9 from two rolls of a standard die and rolling a 2 for the first roll Mutually exclusive events are events that cannot occur together. In this case, rolling a sum of 9 from two rolls of a standard die and rolling 2 for the first roll are two events that cannot possibly occur together. QUESTION 36 1/1 POINTS Fill in the following contingency table and find the number of students who both go to the beach AND go to the mountains.StudentsgotothebeachdonotgotothebeachTotalgotothemountains48donotgotothemountains21Tota l3695 That is correct! $$10 Answer Explanation Correct answers:  $10$10 By using the known totals along the rows and columns you can fill in the rest of the contingency table. For example, looking at the row of totals in the table, we know that the unknown number plus 48 is 95, so the missing number must be 47. Continuing in this way, we can fill in the entire table: StudentsgotothebeachdonotgotothebeachTotalgotothemountains103848donotgotothemountains2 62147Total365995 From this, we can see that the number of students who both go to the beach and go to the mountains is 10. QUESTION 37 1/1 POINTS A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean score out of 100 points was a x¯=77, with a margin of error of 10. Construct a confidence interval for the mean score (out of 100 points) on the final exam. That is correct!$$(67, 87) Answer Explanation Correct answers:  $\left(67,\ 87\right)$(67, 87) A confidence interval is an interval of values, centered on a point estimate, of the form (pointestimate−marginof error,pointestimate+marginof error) Using the given point estimate for the mean, x¯=77 and margin of error 10, the confidence interval is: (77−10,77+10)(67,87) QUESTION 38 1/1 POINTS A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book. Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books. That is correct! $$(0.10, 0.18) Answer Explanation Correct answers:  $\left(0.10,\ 0.18\right)$(0.10, 0.18) By the Empirical Rule, a 95% confidence interval corresponds to a z-score of z=2. Substituting the given values p′=0.14 and σp′=0.02, a confidence interval is (p′−z⋅σp′,p′+z⋅σp′)(0.14−2⋅0.02,0.14+2⋅0.02)(0.14−0.04,0.14+0.04)(0.10,0.18)QUESTION 39 1/1 POINTS The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken? z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Use the table above for the z-score, and be sure to round up to the nearest integer. That is correct! $$14 dog heights Answer Explanation Correct answers:  $14\text{ dog heights}$14 dog heights The formula for sample size is n=z2σ2EBM2. In this formula, z=zα2=z0.025=1.96, because the confidence level is 95%. From the problem, we know that σ=3.7 and EBM=2. Therefore, n=z2σ2EBM2=(1.96)2(3.7)222≈13.15. Use n=14 to ensure that the sample size is large enough. Also, the sample size formula shown above is sometimes written using an alternate format of n=(zσE)2. In this formula, E is used to denote margin of error and the entire parentheses is raised to the exponent 2. Therefore, the margin of error for the mean can be denoted by "EBM" or by "E". Either formula for the sample size can be used and these formulas are considered as equivalent. QUESTION 40 0/1 POINTS Which of the following frequency tables show a skewed data set? Select all answers that apply.That's not right.  Value Frequency 5 1 6 2 7 10 8 11 9 17 10 17 11 15 12 12 13 7 14 7 15 016 1   Value Frequency 5 1 6 3 7 8 8 10 9 13 10 26 11 14 12 12 13 8 14 3 15 116 1   Value Frequency 12 1 13 1 14 3 15 6 16 23 17 29 18 19 19 15 20 3  Value Frequency 0 5 1 16 2 23 3 19 4 22 5 9 6 4 7 2  Answer Explanation Correct answer: Value Frequency 12 1 13 114 3 15 6 16 23 17 29 18 19 19 15 20 3 Value Frequency 0 5 1 16 2 23 3 19 4 22 5 9 6 47 2 Remember that data are left skewed if there is a main concentration of large values with several much smaller values. Similarly, right skewed data have a main concentration of small values with several much larger values. We can see that the following is left skewed because of the concentration of large values with many smaller values: Value Frequency 12 1 13 1 14 3 15 6 16 23 17 29 18 19 19 15 20 3And the following is right skewed because of its concentration of small values with many larger values: Value Frequency 0 5 1 16 2 23 3 19 4 22 5 9 6 4 7 2 The other frequency tables are more balanced and symmetrical. Your answer: Value Frequency 5 1 6 37 8 8 10 9 13 10 26 11 14 12 12 13 8 14 3 15 1 16 1 The data in this table is roughly symmetrical about 10. Value Frequency 12 1 13 1 14 315 6 16 23 17 29 18 19 19 15 20 3 Correct! QUESTION 41 1/1 POINTS A poll was conducted during the final game of the basketball season to determine whether fans wanted to see the defending champions win the game or the challenging team win the game. From the poll, 216 of the 374 residents sampled from urban areas want the defending champions to win the game. In more rural areas, 304 of the 466 residents polled want the defending champions to win the game. Assuming location has nothing to do with team preference, the probability that the data gathered was the result of chance is calculated to be 0.03. What is the correct interpretation of this calculation? That is correct!More people from rural areas want the defending champions to win the game. Exactly 216 out of every 374 urban residents want the defending champions to win the game. The results are statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. The data is not statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. Answer Explanation Correct answer: The results are statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. The probability value calculated is 0.03. This is less than 0.05, so we conclude that the data are statistically significant in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. QUESTION 42 1/1 POINTS In a psychological study aimed at testing a drug that reduces anxiety, the researcher grouped the participants into 2 groups and gave the anxiety-reduction pill to one group and an inert pill to another group. Which group receives the placebo? That is correct!the group that received the anxiety-reduction pill the psychological study all the people in the study the group that received the inert pill Answer Explanation Correct answer: the group that received the inert pill When the experimental units are people, applying treatments that should be inert can actually have effects. So the group that received the inert pill received the placebo. QUESTION 43 1/1 POINTS Which of the following results in the null hypothesis μ≥38 and alternative hypothesis μ<38? That is correct!A fitness center claims that the mean amount of time that a person spends at the gym per visit is at most 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is more than 38 minutes. Answer Explanation Correct answer: A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes. Consider each of the options. The scenario in option B has the null hypothesis μ≥38 based on the words "fewer than" and the fact that the null hypothesis is always stated with some form of equality. QUESTION 44 1/1 POINTS True or False: The more shoes a manufacturer makes, the more shoes they sell. That is correct!True False Answer Explanation Correct answer: False In supply and demand, a company doesn't make a product hoping that someone will buy them, they have a Demand first for their product and then, they produce more of that given product. QUESTION 45 1/1 POINTS Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument. StudentsplaysportsdonotplaysportsTotalplayaninstrument33donotplayaninstrument69Total6267 That is correct! $$34 Answer Explanation Correct answers:  $34$34By using the known totals along the rows and columns you can fill in the rest of the contingency table. For example, looking at the second row in the table, we know that 33 added to the unknown number in the middle is 67, so that unknown number is 34. Continuing in this way, we can fill in the entire table: StudentsplaysportsdonotplaysportsTotalplayaninstrument273360donotplayaninstrument353469T otal6267129 From this, we can see that the number of students who both do not play sports and do not play an instrument is 34. FEEDBACK Question 45 1/1 points Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument. StudentsplaysportsdonotplaysportsTotalplayaninstrument33donotplayaninstrument69Total6267 That is correct! 34$$ 34 - correct Answer Explanation Correct answers:  34 $34$  By using the known totals along the rows and columns you can fill in the rest of the contingency table. For example, looking at the second row in the table, we know that 33 added to the unknown number in the middle is 67, so that unknown number is 34. Continuing in this way, we can fill in the entire table: StudentsplaysportsdonotplaysportsTotalplayaninstrument273360donotplayaninstrument353469T otal6267129From this, we can see that the number of students who both do not play sports and do not play an instrument is 34.     Question 46 · 1/1 points The answer choices below represent different hypothesis tests. Which of the choices are lefttailed tests? Select all correct answers. That is correct!  H0:X=17.3, Ha:X≠17.3   H0:X≥19.7, Ha:X<19.7   H0:X≥11.2, Ha:X<11.2  H0:X=13.2, Ha:X≠13.2   H0:X=17.8, Ha:X≠17.8  Answer Explanation Correct answer: H0:X≥19.7, Ha:X<19.7 H0:X≥11.2, Ha:X<11.2 Remember the forms of the hypothesis tests.  Right-tailed: H0:X≤X0, Ha:X>X0.  Left-tailed: H0:X≥X0, Ha:X<X0.  Two-tailed: H0:X=X0, Ha:X≠X0. So in this case, the left-tailed tests are:  H0:X≥11.2, Ha:X<11.2  H0:X≥19.7, Ha:X<19.7     Question 47 · 1/1 points Assume the null hypothesis, H0, is: Jacob earns enough money to afford a luxury apartment. Find the Type I error in this scenario. That is correct!Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does. Answer Explanation Correct answer: Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when Jacob thinks he does not earn enough money when he really does.     Question 48 · 1/1 points Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are centered at the same point. Normal curve Upper B is narrower and above normal curve Upper A. That is correct!  A has the larger mean.   B has the larger mean.   The means of A and B are equal.  A has the larger standard deviation.   B has the larger standard deviation.   The standard deviations of A and B are equal.  Answer Explanation Correct answer: The means of A and B are equal. A has the larger standard deviation. Remember that the mean of a normal distribution is the x-value of its central point (the top of the "hill"). Therefore, a distribution with a larger mean will be centered farther to the right than a distribution with a smaller mean. Because A and B are centered at the same point, their means are equal. Remember that the standard deviation tells how spread out the normal distribution is. So a high standard deviation means the graph will be short and spread out. A low standard deviation means the graph will be tall and skinny. Because A is shorter and more spread out than B, we find that A has the larger standard deviation.    Question 49 · 1/1 points Hugo averages 62 words per minute on a typing test with a standard deviation of 8 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(62,8). Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is ________. This z-score tells you that x=56 is ________ standard deviations to the ________ (right/left) of the mean, ________. Correctly fill in the blanks in the statement above. That is correct! Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.75. This z-score tells you that x=56 is 0.75 standard deviations to the right of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.75. This z-score tells you that x=56 is 0.75 standard deviations to the left of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.545. This z-score tells you that x=56 is 0.545 standard deviations to the right of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.545. This z-score tells you that x=56 is 0.545 standard deviations to the left of the mean, 62.Answer Explanation Correct answer: Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.75. This z-score tells you that x=56 is 0.75 standard deviations to the left of the mean, 62. The z-score can be found using the formula z=x−μσ=56−628=−68≈−0.75 A negative value of z means that that the value is below (or to the left of) the mean, which was given in the problem as μ=62 words per minute in a typing test. The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. So, typing 56 words per minute is 0.75 standard deviations away from the mean.     Question 50 · 1/1 points The following frequency table summarizes a set of data. What is the five-number summary? Value Frequency 1 6 2 2 3 1 4 1 8 1 9 1 10 1 16 6 20 3 21 1 23 1 24 1 25 1 27 1That is correct! Min Q1 Median Q3 Max 1 2 16 20 27 Min Q1 Median Q3 Max 11 33 2020 2222 27 Min Q1 Median Q3 Max $_1$_ $_2$_ $_6$_ $_20$_ $_27$_ Min Q1 Median Q3 Max $_1$_ $_4$_ $_5$_ $_16$_ $_27$_ Min Q1 Median Q3 Max $_1$_ $_7$_ $_8$_ $_22$_ $_27$_ Answer Explanation Correct answer: Min Q1 Median Q3 Max $_1$_ $_2$_ $_16$_ $_20$_ $_27$_ We can immediately see that the minimum value is $_1$_ and the maximum value is $_27$_. If we add up the frequencies in the table, we see that there are $_27$_ total values in the data set. Therefore, the median value is the one where there are $_13$_ values below it and $_13$_ values above it. By adding up frequencies, we see that this happens at the value $_16$_, so that is the median. Now, looking at the lower half of the data, there are $_13$_ values there, and so the median value of that half of the data is $_2$_. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is $_20$_. $_\color{blue}{1}$_, $_1$_, $_1$_, $_1$_, $_1$_, $_1$_, $_\color{blue}{2}$_, $_2$_, $_3$_, $_4$_, $_8$_, $_9$_, $_10$_, $_\color{blue}{16}$_, $_16$_, $_16$_, $_16$_, $_16$_, $_16$_, $_20$_, $_\color{blue}{20}$_, $_20$_, $_21$_, $_23$_, $_24$_, $_25$_, $_\color{blue}{27}$_ So, the five-number summary is Min Q1 Median Q3 Max $_1$_ $_2$_ $_16$_ $_20$_ $_27$ [Show More]

Last updated: 1 year ago

Preview 1 out of 77 pages