STAT 101 Practice Exam 1 Professor Kari Lock Morgan Duke University

Transcription

1 STAT 101 Practice Exam 1 Professor Kari Lock Morgan Duke University All data used in this exam were collected by students in previous STAT 101 classes for their first project, and all datasets are specific to Duke. Question #1 / 20 Question #2 / 10 Question #3 / 9 Question #4 / 13 Question #5 / 13 Multiple Choice (#6-10) / 10 TOTAL / 75 1

2 1. (20) A reasonably random sample of 104 Duke students were asked how many hours, on average, they spend online networking per week and online reading the news per week. The sample means were 9.0 hours and 3.2 hours, respectively. (a) (2) Suppose you want to test whether Duke students spend more of their online time networking as opposed to reading the news. State the null and alternative hypotheses, defining any parameters used. (b) (3) For this test, the p-value is less than In words, assess the evidence against the null hypothesis (very strong, moderate, little, etc.), and using α = 0.05, state your formal conclusion in context. (c) (3) He also collected data on gender of each student. When we test whether there is a difference between the average amount of time male and female Duke students spend online networking per week, the p-value is In words, assess the evidence against the null hypothesis (very strong, moderate, little, etc.), and using α = 0.05, state your formal conclusion in context. (d) (3) Based on the information you have on this data so far, which of the following intervals are plausible 99% confidence interval for the average difference in time spent networking online per week minus time spent reading news online per week for Duke students? (circle all the intervals that are plausible) (5.1, 6.5) (5.4, 7.0) ( 1.2, 12.8) 2

3 (e) (3) We would like to give a 95% confidence interval for the average number of hours per week that Duke students spend networking online. To do that we generate a bootstrap distribution, shown in Figure 1. Explain in detail how to generate the value for one of the dots shown in the distribution. Figure 1: Bootstrap distribution for average time spent networking online per week (f) (2) Use Figure 1 to estimate (roughly) the standard error of the sample mean online networking time of Duke students per week, for a sample of size 104. (g) (4) Give an approximate 95% confidence interval for the average time spent online networking each week for Duke students, and interpret this interval in context. 3

4 2. (10) A student asked 40 Duke undergraduate heterosexual males the maximum number of inches taller than them that they would like their girlfriend to be. A dotplot of the data is shown in Figure 2. Figure 2: Maximum number of inches taller (a) (2) Calculate the median and interquartile range. (b) (2) Sketch a boxplot for this data. (c) (2) The midrange is defined as the average of the maximum and the minimum. Calculate the midrange for this data. (d) (2) The midrange is a measure of (a) center (b) spread (c) symmetry (e) (2) Is the midrange resistant to outliers? Why or why not? 4

5 3. (9) A student collected data from espn.com on 294 regular season Duke men s basketball games from , and produced the following table: Win Loss Home Away Table 1: 294 regular season Duke men s basketball games, (a) (3) We are interested in the difference in the proportions of wins between home and away games. Calculate the relevant sample statistic. (b) (3) We want to test whether Duke men s basketball has a higher chance of winning at home rather than away. A randomization distribution based on 10,000 simulations in shown in Figure 3b. What can you conclude about the p-value? Explain. Figure 3: Duke Men s Basketball: Randomization Distribution (c) (3) Based on the data in Table 1 and Figure 3b, can we conclude that the Cameron Crazies help the team? Why or why not? 5

6 4. (13) You want to see if listening to music while you study is helpful, detrimental, or neutral for Duke students. (a) (3) Briefly explain how you would collect data to answer this question. (b) (2) A student collected data on this last semester, and when testing these hypotheses, he got a p-value of Using α = 0.05, state the conclusion in context. (c) (2) If listening to music does not affect studying, did he make an error? If so, what type? (d) (2) If listening to music does affect studying, did he make an error? If so, what type? (e) (2) How could the student have decreased his chance of making a Type I error? (f) (2) How could the student have decreased his chance of making a Type II error? 6

7 5. (13) A student stood on Duke s campus with a large poster board with the question Do you feel comfortable with Duke s social environment?. 113 Duke students stopped to answer the question, and more people responded yes than no. A 95% confidence interval based on 1000 bootstrap samples was found to be (0.66, 0.82). (a) (2) Give the sample statistic, using correct notation. (b) (2) Define the parameter this interval is designed to capture, using correct notation. (c) (6) Circle the interval you would be mostly likely to see, under each of the following three changes: Increase the sample size to 200 students: Increase the confidence level to 99%: (0.63, 0.85) (0.66, 0.82) (0.71, 0.77) (0.63, 0.85) (0.66, 0.82) (0.71, 0.77) Increase the number of bootstrap samples to 10,000: (0.63, 0.85) (0.66, 0.82) (0.71, 0.77) (d) (3) If this study were to be repeated in the same way many times, do you think that more than 95%, about 95%, or less than 95% of the 95% confidence intervals would capture the parameter you defined in 5b? Explain. 7

8 6. (2) The statistic x/m can be used as a measure of skewness. If this statistic is less than 1, the distribution is most likely (a) Right-skewed (b) Left-skewed (c) Symmetric 7. (2) If one variable decreases as the other decreases, the correlation is most likely (a) Positive (b) Negative (c) Zero 8. (2) Two variables, Greek/Non-Greek and GPA, were both collected on a reasonably random sample of 78 Duke students. When testing for a difference in GPA between Greek and non-greek students, the sample difference (non-greek Greek) was 0.11, and the p-value was Which of the following is true? (a) 0.07 is the probability of getting a sample difference in mean GPA between Greek and non-greek members as extreme as (b) 0.07 is the probability of getting a sample difference in mean GPA between Greek and non-greek members as extreme as 0.11, if there really is no difference. (c) 0.07 is the probability that there is a difference in average GPA between Greek member and non-greek members at Duke. (d) 0.07 is the probability that there is not a difference in average GPA between Greek member and non-greek members at Duke. (e) 0.07 is the probability that the difference in average GPA between Greek and non-greek members is as extreme as (2) Which association is broken by randomizing cases into treatment groups in a randomized experiment? (a) the association between the explanatory variable and a confounding variable (b) the association between a confounding variable and the response variable (c) the association between the explanatory variable and the response variable 10. (2) Which association is broken by re-randomizing units into treatment groups (reallocating) for a randomization test? (a) the association between the explanatory variable and a confounding variable (b) the association between a confounding variable and the response variable (c) the association between the explanatory variable and the response variable 8