4-5 Simulations for Hypothesis Tests 195 4. Simulating Body Temperatures If Example 1 is repeated with a different sample and it is found that for 100 randomly generated samples, 40 of these generated samples have a mean that is as extreme as the mean of the actual sample, what should be concluded about the assumed mean of 98.6°F? In Exercises 5–8, describe the simulation procedure. (For example, to simulate 10 births, use a random number generator to generate 10 integers between 0 and 1 inclusive, and consider 0 to be a male and 1 to be a female.) 5. Brand Recognition The probability of randomly selecting an adult who recognizes the brand name of McDonald’s is 0.95 (based on data from Franchise Advantage). Describe a procedure for using software or a TI-83/84 Plus calculator to simulate the random selection of 50 adult consumers. Each individual outcome should be an indication of one of two results: (1) The consumer recognizes the brand name of McDonald’s; (2) the consumer does not recognize the brand name of McDonald’s. 6. Lefties Ten percent of people are left-handed. In a study of dexterity, 15 people are randomly selected. Describe a procedure for using software or a TI-83>84 Plus calculator to simulate the random selection of 15 people. Each of the 15 outcomes should be an indication of one of two results: (1) Subject is left-handed; (2) subject is not left-handed. 7. Tom Brady Tom Brady gained fame as the quarterback for the New England Patriots until 2020 when he left. As of this writing, he threw 9375 passes and 6004 of them were caught, so his success rate is 0.640. Describe a procedure for using software or a TI-83>84 Plus calculator to simulate his next pass. The outcome should be an indication of one of two results: (1) The pass is caught; (2) the pass is not caught. 8. Simulating Hybridization When Mendel conducted his famous hybridization experiments, he used peas with green pods and yellow pods. One experiment involved crossing peas in such a way that 75% of the offspring peas were expected to have green pods, and 25% of the offspring peas were expected to have yellow pods. Describe a procedure for using software or a TI-83>84 Plus calculator to simulate 20 peas in such a hybridization experiment. Each of the 20 individual outcomes should be an indication of one of two results: (1) The pod is green; (2) the pod is yellow. In Exercises 9–12, use a suitable technology to conduct the simulation. 9. Body Temperatures Repeat Example 1 using these statistics from the 8 AM temperatures on Day 2 from Data Set 5 “Body Temperatures”: n = 70, x = 97.49°F, s = 0.70°F. As in Example 1, assume that the temperatures are from a normally distributed population. 10. Body Temperatures Repeat Example 1 using these statistics from hypothetical data with these statistics: n = 50, x = 98.5°F, s = 0.7°F. Assume that the sample temperatures are from a normally distributed population. 11. Got a Minute? Students of the author estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Assuming that the times are from a normally distributed population, use a simulation to determine whether these times are from a population with a mean equal to 60 seconds. 69 81 39 65 42 21 60 63 66 48 64 70 96 91 65 12. IQ Scores New York City cab drivers are randomly selected for IQ tests, and the results are listed below. Assuming that IQ scores are from a normally distributed population, use a simulation to determine whether these IQ scores are from a population with a mean equal to 100. 88 115 74 123 93 98 99 93 82 106
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