AP Statistics 2021 Free-Response Questions (2)

Begin your response to QUESTION 1 on this page. STATISTICS SECTION II Total T ime—1 hour and 30 minutes 6 Questions Part A Questions 1-5 Spend about 1 hour and 5 minutes on this part of the exam. Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1. The length of stay in a hospital after receiving a particular treatment is of interest to the patient, the hospital, and insurance providers. Of particular interest are unusually short or long lengths of stay. A random sample of 50 patients who received the treatment was selected, and the length of stay, in number of days, was recorded for each patient. The results are summarized in the following table and are shown in the dotplot. Length of stay ( days ) 5 6 7 8 9 12 21 Number of patients 4 13 14 11 6 1 1 ( a ) Determine the five-number summary of the distribution of length of stay. GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. © 2021 College Board. Visit College Board on the web: collegeboard.org. 4 AP ® Statistics 2021 Free-Response Questions Min 5 Q1 6 med 7 Q3 8 max 21

Continue your response to QUESTION 1 on this page. ( b ) Consider two rules for identifying outliers, method A and method B. Let method A represent the 1.5 ¥ IQR rule, and let method B represent the 2 standard deviations rule. ( i ) Using method A, determine any data points that are potential outliers in the distribution of length of stay. Justify your answer. ( ii ) The mean length of stay for the sample is 7.42 days with a standard deviation of 2.37 days. Using method B, determine any data points that are potential outliers in the distribution of length of stay. Justify your answer. ( c ) Explain why method A might identify more data points as potential outliers than method B for a distribution that is strongly skewed to the right. GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. © 2021 College Board. Visit College Board on the web: collegeboard.org. 5 AP ® Statistics 2021 Free-Response Questions I QR Q Q 8 6 2 Q 1 St IQ R 3 3 any value below 3 considered outlier Q 3 1 SKI QR 11 any value above 11 considered outlier meant 2xsp 7.42 212.32 zoo 12.16 anything outside this interval is considered an outlier Mean pulled more toward the extreme values in the longer right tail for a strongly right skewed distribution than the median The larger the increase in standard deviation relative to theIOR results in a greater increase inthe range of non outliervalues for method B

Begin your response to QUESTION 2 on this page. 2. Researchers will conduct a year-long investigation of walking and cholesterol levels in adults. They will select a random sample of 100 adults from the target population to participate as subjects in the study. ( a ) One aspect of the study is to record the number of miles each subject walks per day. The researchers are deciding whether to have subjects wear an activity tracker to record the data or to have subjects keep a daily journal of the miles they walk each day. Describe what bias could be introduced by keeping the daily journal instead of wearing the activity tracker. GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. © 2021 College Board. Visit College Board on the web: collegeboard.org. 6 AP ® Statistics 2021 Free-Response Questions keeping a daily journal could result in a bias that would be avoided by activity traders The use of a daily journal may result in a systematic under or over reporting of daily miles walked

Continue your response to QUESTION 2 on this page. During the course of the study, the subjects will have their cholesterol levels measured each month by a doctor. The researchers will perform a significance test at the end of the study to determine whether the average cholesterol level for subjects who walk fewer miles each day is greater than for those who walk more miles each day. ( b ) Selecting a random sample creates a reasonable representative sample of the target population. Explain the benefit of using a representative sample from the population. ( c ) Suppose the researchers conduct the test and find a statistically significant result. Would it be valid to claim that increased walking causes a decrease in average cholesterol levels for adults in the target population? Explain your reasoning. GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. © 2021 College Board. Visit College Board on the web: collegeboard.org. 7 AP ® Statistics 2021 Free-Response Questions Representative sample neccesay in order to make a generalization about the target population There is an association between cholesterol level and amount of walking in the target population A casual inferene cannot be made there is a lack of random assignment of treatments to subjects which marks that causation cannotoccur