AP® is a trademark registered by the College Board, which was not involved in the production of, and does not endorse, this exam. AP® STATISTICSSECTION ITime --- 1 hour and 30 minutesNumber of questions --- 40 Percent of total grade --- 50 Directions: Solve each of the following problems, using the available space for scratch work. Decide which is the best of the choices given and fill in the corresponding box on the answer sheet. Do not spend too much time on any one problem. 1.Academia High School co llected heights of students in their intramural basketball league. The boxplot and statistics below provide a summary of the distribution of heights, in inches. Height (in inches)MeanStd DevMinimumQ1MedianQ3Maximum68.24.216265677179Which conclusion about the distribution is most plausible? (A)50% of the students are taller than 68.2 inches. (B)75% of the students are taller than 71 inches. (C)There are more students between 68.2 inches and 79 inches than are between 62 inches and 68.2 inches. (D)Less than 25% of the students have heights between 68.2 and 71 inches. (E)The height that occurs most frequently is 67 inches.
-2- 2.Researchers conducting a study of the effectiveness of Tamiflu for reducing the duration of flu symptoms recruited 50 subjects who agreed to report to the researchers' lab within 24 hours of getting flu symptoms. Half of the subjects were randomly assigned to take a full dosage of Tamiflu and the other half received a placebo. The time (in hours) to alleviation of all flu symptoms for the two groups are compared in the back-to-back stemplot below. TamifluPlacebo855695520078865000805575530900266893010044570110225120921358148156Key: 15|6 = 156 hours Which of the following statements is true about the shapes of the distributions of recovery times? (A)The distributions of recovery times for the Tamiflu and placebo groups are both symmetric.(B)The distributions of recovery times for the Tamiflu and placebo groups are both skewed to the left. (C)The distributions of recovery times for the Tamiflu and placebo groups are both skewed to the right.(D)The distribution of recovery times for the Tamiflu group is skewed to the left, and the distribution of recovery times for the placebo group is skewed to the right. (E)The distribution of recovery times for the Tamiflu group is skewed to the right, and the distribution of recovery times for the placebo group is skewed to the left.
-3- 3.Last week, Mrs. Thomas, the AP Statistics teacher at Green Valley High School, gave her students an assessment on material they had recently studied. The students' scores on the assessment followed an approximately normal distribution with mean 83.54 and standard deviation 11.21. Andrew, a student in Mrs. Thomas' class, had a standardized score of z = 0.88. What was Andrew's score on the test, and in which quarter of the distribution would Andrew's score fall?(A)73.68; his score would fall in the first quarter because it is below the first quartile(B)73.68; his score would fall in the second quarter because it is between the first quartile and the median(C)84.42; his score would fall in the fourth quarter because it is above the third quartile (D)93.40; his score would fall in the fourth quarter because it is above the third quartile (E)93.40; his score would fall in the first quarter because it is below the first quartile4.A study was conducted to test the effect of product price and display level on supermarket sales. At one supermarket, the price level (regular, reduced price, and at cost to supermarket) and the display level (normal display space, normal display space plus end of aisle display, and twice the normal display space) were varied to determine if they had any effect on the weekly sales of a particular supermarket product. Each combination of price and display was recorded. Each combination was used three times over the course of the experiment. Identify the treatments used in this experiment. (A)The three price levels used by the supermarket(B)The three display levels used by the supermarket(C)The supermarket (D)The weekly sales for each of the weeks(E)The nine combinations of price and display levels used by the supermarket
-4- 5.Consider the following residual plot for the least squares regression line of y versus x. Which of the following is an appropriate conclusion based on the residual plot? (A)There is a pattern in the residual plot, so there will not be a linear trend in the scatterplot of yversus x. (B)There is a strong, positive linear relationship between x and y because there is no pattern in the residual plot. (C)Because there is no pattern in the residual plot, there will be a linear trend apparent in the scatterplot of y versus x. (D)There will be a linear trend apparent in the scatterplot of y versus x, but the data values will tend to fall closer to the regression line for smaller values of x than for larger values of x. (E)Because none of the residuals equal zero, the least squares regression line will not be useful for prediction. 6.Before opening a new restaurant, a chef wants to gather information about the eating habits of the local residents. He randomly selects 1000 households from all households in the area and mails a questionnaire to them. Of the 1000 surveys mailed, he receives 150 back. Which of the following is the most obvious concern with how this information is gathered? (A)The 1000 selected households are not a simple random sample of households. (B)Mailing questionnaires instead of conducting in-person interviews produces a convenience sample. (C)Those who chose to respond to the survey may have different eating habits from those who did not respond. (D)Only residents from the local area were polled.(E)The chef must conduct a census in order to avoid all sources of bias.
-5- 7.Does the color of cards affect a person's ability to sort the cards? Twelve volunteers were asked to sort two sets of 200 cards into two piles. One set of cards were bright red and bright green. The other set of cards were black and white. The order (red/green first or black/white first) was determined by a coin toss with ample time between the two tasks to lessen the effect of practice. The time (in seconds) to complete each of the two tasks are given in the table below.Completion time (in seconds)Volunteer123456789101112Red/Green148198193128206158214167207173190139Black/White136182186133198162196163199161183144Assuming the conditions for inference are met, what statistical test should be used to determine if there is a significant difference in the mean time required to sort the two sets of cards?(A)A chi -square goodness-of-fit test(B)A chi -square test of independence(C)A matched-pairs t-test for means(D)A two-sample t-test for means(E)A linear regression t-test 8.Consider a tack like the one pictured below. When dropped on a table, the tack can land either point down or point up. Suppose we assume that P(tack lands point down) = 0.40. Which of the following must be true? (A)If the tack is dropped 50 times and lands point down only 10 times, then it must land point down more than 40% of the time in the next 50 drops. (B)If the tack is dropped on a table 10 times, it will land point down 4 times. (C)If the tack is dropped on a table 1,000,000 times, it will land point down 400,000 times. (D)Over many tack drops, the proportion that land point down will be very close to 0.40. (E)The tack landed point down twice in a simple random sample of 5 people who dropped it on a table.
-6- 9.Let X be a random variable that has a skewed right distribution with mean 𝜇𝜇 = 10 and standard deviation 𝜎𝜎 = 10. Which of the following histograms could display the distribution of the sample mean 𝑥𝑥̅ from many random samples of size 400 from this population? (A)(B)(C)(D)(E)
