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 minutes Number 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.The histogram below shows the distribution of annual growth rate in travel spending for 52 companies in the United States. After creating this graph, it was discovered that the values for the companies with the 20 largest reported annual growth rates were miscalculated. In fact, each of these top 20 companies should have a higher value of annual growth rate than was previously reported. Which of the following statements must be true? (A)If you were to make a graph with the corrected values, the graph would be skewed to the left. (B)If you were to make a graph with the corrected values, the graph would be symmetric.(C)If you were to calculate the median with the corrected values, the new median would be greater than the old median.(D)If you were to calculate the interquartile range (IQR) with the corrected values, the new IQR would be the same as the old IQR.(E)If you were to find the value of the third quartile (Q3) with the corrected values, the new Q3 would be greater than the old Q3.
-2- 2.The council leaders of a small town would like to determine the average number of people living in each household. To accomplish this, they send a questionnaire to each residence listed in the town address records, asking the head of the household to record the number of people living in the dwelling. They follow this up with visits to those households that have not responded to the questionnaire until the data collection process is complete. Which of the following is the best description of the method for data collection used by the council leaders?(A)A convenience sample(B)A simple random sample(C)A stratified random sample(D)A cluster random sample (E)A census 3.A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation 𝑦𝑦�=400−0.08𝑥𝑥. Which of the following best describes the meaning of the slope of the least-squares regression line?(A)The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B)The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C)The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D)The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (E)Approximately 8% of the variability in the percentage increase in lung volume when inhaling is explained by its linear relationship with the percentage of carbon dioxide in the atmosphere.
-3- 4.A student was interested in investigating whether female or male students at her school tend to have quicker reaction times. The students in her study played an online game that measured reaction time by how quickly you press stop after an orange sign appears. The timing of the appearance of the orange signs is random. The reaction times (in seconds) for the male and female students at her school that volunteered to take part in the study are displayed in the boxplots below.Based on the boxplots, which of the following statements must be true? (A)At least 75% of the female reaction times are greater than the maximum reaction time for the males.(B)If the highest reaction time for the males was removed, the distribution of male times would be approximately normally distributed.(C)There is more variability in the highest 25% of reaction times for the female students than in the highest 25% of times for the male students. (D)More female students took part in the study than male students.(E)The mean reaction time for the male students is greater than the mean reaction time for the female students
-4- 5.The monthly allowance in dollars for a random sample of high school students is displayed in the cumulative frequency graph below. Based on this graphical display, which of the following statements is justified? (A)A greater percentage of these students have monthly allowance between $50 and $75 than between $175 and $200. (B)The median monthly allowance for these students is about $100.(C)A greater percentage of these students have an allowance above $100 than below $100. (D)The minimum monthly allowance for these students is greater than $10.(E)The graph of the cumulative percent of monthly allowance for these students is skewed to the right.
-5- 6.Doctors are now considering prescribing social activities as a way to increase the overall health of their patients. A random sample of adult men with heart disease were prescribed two sessions a week consisting of 30 minute group discussions on lifestyle changes followed by 45 minute golf lessons. As an indicator of overall health, each subjects' grip strength was measured at the start and end of the six-week study, with higher grip strength indicating better health. Let 𝜇𝜇B represent the population mean grip strength before participating in prescribed social activities, 𝜇𝜇A represent the population mean grip strength after participating in prescribed social activities, and 𝜇𝜇D represent the population mean difference in grip strength (before – after). Which of the following would be the null and alternative hypotheses for this study? (A)H0 : 𝜇𝜇B = 𝜇𝜇A and Ha : 𝜇𝜇B > 𝜇𝜇A(B)H0 : 𝜇𝜇B = 𝜇𝜇A and Ha : 𝜇𝜇B≠𝜇𝜇A(C)H0 : 𝜇𝜇𝐷𝐷 = 𝜇𝜇B−𝜇𝜇A and Ha : 𝜇𝜇𝐷𝐷 < 𝜇𝜇B−𝜇𝜇A(D)H0 : 𝜇𝜇𝐷𝐷> 0 and Ha : 𝜇𝜇𝐷𝐷 = 0(E)H0 : 𝜇𝜇𝐷𝐷 = 0 and Ha : 𝜇𝜇𝐷𝐷 < 07.In 2013, Ace Metrix gathered a random sample of 1200 television ads and found that 180 (or 15%) featured a celebrity. They created a confidence interval to estimate the proportion of all ads that feature a celebrity to within 2.7%. Based on this interval, which of the following must be true? (A)Approximately 2.7% of all television ads were sampled.(B)With 97.3% confidence, 15% of all television ads feature a celebrity.(C)It is plausible that 19% of all television ads feature a celebrity.(D)It is plausible that 13% of all television ads feature a celebrity.(E)Between 12.3% and 17.7% of all celebrities have been featured in television ads.
-6- 8.As a reward for completing a reading challenge, two elementary school students are allowed to select one ice cream bar from a box containing 12 bars. The box contains four chocolate bars (C), four strawberry bars (S), and four vanilla bars (V). Suppose the two students select their ice cream bars at random. The probability for each possible selection is given in the table below. Bars SelectedCC CV CS SCSSSVVCVSVVProbability111433433433111433433433111Find the expected number of vanilla bars selected.(A)13bars (B)23bars (C)611bars (D)1913bars (E) 1 bar
