AP1.13 The frequency table summarizes the distribution of time that 140 patients at the emergency room AP1.14 Boxplots of two data sets are shown. of a small-city hospital waited to receive medical attention during the last month. Plot 1 Waiting time Plot 2 Frequency Less than 10 minutes 5 At least 10 but less than 20 minutes Based on the boxplots, which of the following 24 At least 20 but less than 30 minutes is true? 45 At least 30 but less than 40 minutes (a) The range of both plots is about the same. 38 At least 40 but less than 50 minutes (b) The means of both plots are approximately equal. 19 At least 50 but less than 60 minutes (c) Plot 2 contains more data points than Plot 1. At least 60 but less than 70 minutes d) The medians are approximately equal. e) Plot 1 is more symmetric than Plot 2. Which of the following represents possible values for the median and IOR of waiting times for the emergency room last month? (a) median = 27 minutes and IQR = 15 minutes (b) median = 28 minutes and IQR = 25 minutes (c) median = 31 minutes and IQR = 35 minutes (d) median = 35 minutes and IQR = 45 minutes (e) median = 45 minutes and IQR = 55 minutes Section II: Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. AP1.15 The manufacturer of exercise machines for fitness (c) Which machine should be chosen if the company centers has designed two new elliptical machines wants to advertise it as achieving the most consistent that are meant to increase cardiovascular fitness. gain in cardiovascular fitness? Explain your reasoning. The two machines are being tested on 30 volun- teers at a fitness center near the company's head- (d) Give one reason why the advertising claims of the quarters. The volunteers are randomly assigned company (the scope of inference) for this experiment to one of the machines and use it daily for two would be limited. Explain how the company could months. A measure of cardiovascular fitness is broaden that scope of inference. administered at the start of the experiment and AP1.16 Those who advocate for monetary incentives in a again at the end. The following stemplot contains work environment claim that this type of incen- the differences (After - Before) in the two scores tive has the greatest appeal because it allows the for the two machines. Note that greater differences winners to do what they want with their winnings. indicate larger gains in fitness. Those in favor of tangible incentives argue that Machine A| | Machine B money lacks the emotional appeal of, say, a week- end for two at a romantic country inn or elegant 2 54 Key: 2 | 1 represents a hotel, or a weeklong trip to Europe. NN - 876320 159 difference (After - Before) A few years ago a national tire company, in an effort 97411 2489 of 21 in fitness scores. to improve sales of a new line of tires, decided to 51 257 test which method- offering cash incentives or 359 offering non-cash prizes such as vacations -was more successful in increasing sales. The company (a) Write a few sentences comparing the distributions had 60 retail sales districts of various sizes across the of cardiovascular fitness gains from the two elliptical country and data on the previous sales volume for machines. each district. (b) Which machine should be chosen if the company (a) Describe a completely randomized design using the wants to advertise it as achieving the highest overall 60 retail sales districts that would help answer this gain in cardiovascular fitness? Explain your reasoning