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

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

Begin your response to QUESTION 3 on this page. 3. To increase morale among employees, a company began a program in which one employee is randomly selected each week to receive a gift card. Each of the company’s 200 employees is equally likely to be selected each week, and the same employee could be selected more than once. Each week’s selection is independent from every other week. ( a ) Consider the probability that a particular employee receives at least one gift card in a 52 -week year. ( i ) Define the random variable of interest and state how the random variable is distributed. ( ii ) Determine the probability that a particular employee receives at least one gift card in a 52 -week year. Show your work. 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. 8 AP ® Statistics 2021 Free-Response Questions y of gift cards that a particular employee relieves in a sa week year x has a binomial distribution with n 52 repeated independent trials and probability of success p 0.005 for each trial too us p of being selected each week to recieve gift card P x2 I P x D I 1 o.oosjco.us 1 0.7705 oi

Begin your response to QUESTION 4 on this page. 4. The manager of a large company that sells pet supplies online wants to increase sales by encouraging repeat purchases. The manager believes that if past customers are offered $10 off their next purchase, more than 40 percent of them will place an order. To investigate the belief, 90 customers who placed an order in the past year are selected at random. Each of the selected customers is sent an e-mail with a coupon for $10 off the next purchase if the order is placed within 30 days. Of those who receive the coupon, 38 place an order. ( a ) Is there convincing statistical evidence, at the significance level of a = 0.05 , that the manager’s belief is correct? Complete the appropriate inference procedure to support your answer. 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. 10 AP ® Statistics 2021 Free-Response Questions p proportion of all customers ofthe pet supply company who would place an order within 30 daysafter recieving an email with a coupon for 10 off the next purchase Ho p 0.40 Ha p so.to we use aone sample z test for a population proportion Random s he have an Srs if 90 customers Independents ion s co ao an more than 900 customers Normal s up 5 ao o 36 210 no p s ao co 6 Sy 1101 P Yo 0.422 z gj f o.no plz 0.430 0.33 Since our p value 0.333 2 05 we fail to reject the Ho There is not statistically significant evidence that the manager's belief is correct

Continue your response to QUESTION 4 on this page. ( b ) Based on your conclusion from part ( a ) , which of the two errors, Type I or Type II , could have been made? Interpret the consequence of the error in context. 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. 11 AP ® Statistics 2021 Free-Response Questions Since the null hypothesis was not rejected a Type II error could have been made A Type II error is when he fail to reject the null hypothesis when it is actually false In this case a Type II error is made by failing to reject the null hypothesis that 40 percent or less of all customers of the pet supply company would place an order within 30 days after relieving an e mail with a coupon for 10 off the next purchase when in fact more than 40 percent world do so

Continue your response to QUESTION 5 on this page. ( b ) Consider the values in the table. ( i ) Construct a segmented bar chart of relative frequencies based on the information in the table. ( ii ) Which city had the smallest proportion of teens who consumed a soft drink in the previous week? Determine the value of the proportion. ( c ) Consider the inference procedure that is appropriate for investigating whether there is a difference among the three cities in the proportion of all teens who consumed a soft drink in the past week. ( i ) Identify the appropriate inference procedure. ( ii ) Identify the hypotheses of the test. 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. 13 AP ® Statistics 2021 Free-Response Questions im mmmm mmmmm Baltimore s II 0.804 netwit 1 5 0.741 san Diego o San Diego has the smallest proportion coos of teens who consumed a soft drink in the previous week since data collected fwm independent random samples from the3 cities we should use a Chi square testfor homogeneity Io there is no difference in the proportion of all teens who consumed a soft drink in the past week across the three cities 1 inthepas.tw kacvosthethrecitiesy

Begin your response to QUESTION 6 on this page. Part B Question 6 Spend about 25 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. 6. Attendance at games for a certain baseball team is being investigated by the team owner. The following boxplots summarize the attendance, measured as average number of attendees per game, for 47 years of the team’s existence. The boxplots include the 30 years of games played in the old stadium and the 17 years played in the new stadium. ( a ) Compare the distributions of average attendance between the old and new stadiums. 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. 14 AP ® Statistics 2021 Free-Response Questions the team tended to have a higher average per game attendance duringyears in the new stadium because the median value of about 2s no attendees per game is greater than the median value of abut 16 ooo attendees per game the IQ Rs are similar which indicates that variability in average per game attendance is similar during the years in the two stadiums but the range of average per game attendance is slightly larger during the years in the new stadium there are no years with average per game attendance identified as an outlier for either stadium

Continue your response to QUESTION 6 on this page. ( c ) Consider the following scatterplots. ( i ) Graph I shows the average attendance versus number of games won for each year. Describe the relationship between the variables. ( ii ) Graph II shows the same information as Graph I, but also indicates the old and new stadiums. Does Graph II suggest that the rate at which attendance changes as number of games won increases is different in the new stadium compared to the old stadium? 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. 16 AP ® Statistics 2021 Free-Response Questions Graph I shows a strong positive linear relationship between average per game attendance and the number of games won I indicating that the rates are about the same for the two stadiums since the slopes are the same