University Of Maryland - University College > STAT 200 MIDTERM EXAM ANSWERS (2021) - (all solutions 100% correct)

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Stat 200 Midterm Exam Spring 1 2021 1. You are interested in the average home price in Clarksville in 2018. To gather your sample, you breakdown Clarksville into these groups: River area, Rossview, No... rtheast, Ft. Campbell, and Sango. You randomly choose two of these areas and survey all homes sold in those two areas. What type of sampling is this? A. Convenience B. Stratified C. Cluster D. Systematic 2. A campaign manager is interested in the amount of votes her candidate would receive. Would an experimental or observational study design be more appropriate? A. An observational study because the number of votes cannot be controlled. B. An observational study because her candidate cannot be directly controlled. C. An experimental study with the amount of votes as the controlled factor. D. An experimental study with the voters as the controlled factor. 3. We study but are truly interested in . A. explanatory variables; response variables B. populations; samples C. samples; populations D. SRS; SME E. SME; SRS 4. The small subset from the large group that we actually study is called the . A. sample B. population C. statistic D. SRS E. inference 5. The physical center of a set of numbers. A. Q1 B. Q2 C. mean D. Q3 E. mode 6. An “event” is A. always contains more than one outcome B. an unexpected outcome C. an outlying outcome D. a subset of the sample space 7. Required for disjoint (mutually exclusive) events A. P(A|B) = P(A) B. P(A ∩ B) = 0 C. P(A U B) = 0 D. P(A|B) > 1.0 E. P(A|B) = P(B) 8. Example of : red, yes, blonde Example of : number of computers in your home, people you have dated, shoes in your closet Example of : age, distance traveled, minutes spent studying A. discrete, categorical, continuous B. discrete, continuous, categorical C. categorical, discrete, continuous D. categorical, continuous, discrete E. continuous, discrete, categorical 9. Caleb collected data from a random sample of 200 students in his high school asking whether or not they spend more than 30 minutes per day reading. Based on the results, he reports that 46% of the high school students in the nation spend more than 30 minutes per day reading. What type of error did Caleb commit? A. None. Caleb is perfect. B. Non-sampling error C. Sampling error D. Random error 10. Subjective probability A. depends on the medical conditions. B. is the based on a person’s expertise. C. changes the initial probability based on additional information given. D. depends on the weather conditions. 11. What is the coefficient of determination? A. r B. r2 C. y D. x E. ^y 12. Which of the above graphs appears to contain an outlier? A. Both B. Neither C. A D. B 13. Total area under the curve is always . A. 68% B. 1% C. 1 D. 0.95 E. 99.7% 14. When extrapolating, you will ALWAYS yield . A. unreliable results. B. reasonable results. C. reliable results. D. unreasonable results. 15. According to the CLT A. As n increases, the distribution of the sample becomes an approximately normal distribution. B. As n decreases, the distribution of the sample becomes an approximately normal distribution. C. The population distribution must be normal for the distribution of the sample to be an approximately normal distribution. D. The sample distribution must be normal for the population distribution to be an approximately normal distribution. Use the following steam-and-leaf plot to answer the next two questions. Stem-and-leaf of excessive absences Leaf Unit = 1.0 1 1 1 44566 2 0 16. How many students missed more than 10 days? Use the following boxplots to answer the next two questions. 17. Which graph has the largest median? A. xx B. yy C. zz D. All E. None 18. Which graph contains the most outliers? A. xx B. yy C. zz D. All E. None Use the following histograms for the next two questions. 19. Which histogram has the smallest standard deviation? A. A B. B C. C D. They are all the same 20. Which graph appears to be skewed to the right? A. A B. B C. C D. All E. None Fill in the following Frequency Chart and use on the next three questions: You took a SRS of UMGC students on Clay and found the following information for the amount of speeding tickets they have received. Amount of Tickets Frequency Relative Frequency Cumulative Relative Frequency 0-2 7 7/25 or .28 .28 3-5 10 10/25 or .4 .68 6-8 3 3/25 or .12 .8 9-11 3 3/25 or .12 .92 12+ 2 2/25 or .08 1.0 TOTAL 25 25/25 or 1 1.0 21. Fill in all the relative frequencies. 22. Fill in all the cumulative frequencies. 23. For the above scenario, what is the sample? A. All UMGC students B. All students attending a university C. All Americans in Germany D. The 25 random students surveyed E. All UMGC students in Wiesbaden 24. Your company plans to invest in a particular project. There is a 25% chance that you will lose $30,000, a 60% chance that you will break even, and a 15% chance that you will make $45,000. What is your companies expected value of this investment? You are interested in studying if sex affects whether college students “occasionally smoke” or “occasionally drink”. You obtain the following data. Use it to answer the next 2 questions. 15 10 6 5 25. What proportion of your sample drinks occasionally? 26. What type of graph is this? A. Bar chart D. Histogram B. Pie chart E. Pareto chart C. Dot plot You are interested in the average number of credit hours freshman take in their first semester at UMGC. You take a SRS and obtain the following data: HOURS 19 18 15 15 15 14 14 12 12 11 6 27. What is the sample mean of HOURS? 28. What is the population standard deviation for HOURS? 29. What is the IQR for HOURS? 30. What value(s) in the list is/are an outlier for list EEE? Bananas have an average 29.65 gram of carbohydrates with a standard deviation of 7.1 grams. Forty bananas are selected at random. 31. How are the sample means distributed? A. Normal B. Bimodal C. Approximately Normal D. Binomially 32. Find μx´ ? 33. What is the probability that the sample mean will be less than 28.5 grams? 34. What is the probability that the average carbohydrates for a sample mean will be between 23.9 and 30.1 grams? Caleb has missed much of his Stat 200 class. He is given a quiz with 6 questions on it and must guess randomly at the answer on each question. Each question has 4 answer choices. You may use the following probability distribution table if you would like. x 0 1 2 3 4 5 6 P(X=x) .178 .356 .297 .132 .033 .004 .00024 P(X≤x) 35. What is the probability of answering three questions correctly? 36. What is the probability of answering at most three correctly? 37. What is the probability of answering less than three correctly? 38. What is the probability of answering at least three correctly? 39. What is the standard deviation of the distribution? 40. What is the mean of this distribution? Consider the sample space containing all of the possible outcomes of rolling two dice. 41. Let event A be the probability that the either die shows a three. Find P(A). 42. Let event B be the probability that sum of the two dice is less than 9. What is the probability that B occurs given that A has occurred? 43. Are event A and event B independent? B. Yes, because P ( A ∣ B )≠ P( B∣ A ) . C. Yes, because both A and B can simultaneously occur. D. No, because P ( A ∣ B )≠ P( B∣ A ) . E. No, because P (B ∣ A )≠ P( B) . You are leading a study to determine if administering Botox will have any effect on patients who are experiencing night sweats. Given this partial contingency table: Meds No Sweat Sweat total Botox 84 44 128 Placebo 20 24 44 total 104 68 172 44. [Show More]

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