CHAPTER 10 STATISTICAL INFERENCE FOR TWO SAMPLES

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with the manufacturers processes that 1 5 psi and 2 4 psi. A random sample of 20 test specimens from each manufacturer results in x1 88 psi and x2 91 psi, respectively. (a) Using a 90% con dence interval on the difference in mean breaking strength, comment on whether or not there is evidence to support the claim that manufacturer 2 produces yarn with higher mean breaking strength. (b) Using a 98% con dence interval on the difference in mean breaking strength, comment on whether or not there is evidence to support the claim that manufacturer 2 produces yarn with higher mean breaking strength. (c) Comment on why the results from parts (a) and (b) are different or the same. Which would you choose to make your decision and why 10-73. The Salk polio vaccine experiment in 1954 focused on the effectiveness of the vaccine in combatting paralytic polio. Because it was felt that without a control group of children there would be no sound basis for evaluating the ef cacy of the Salk vaccine, the vaccine was administered to one group, and a placebo (visually identical to the vaccine but known to have no effect) was administered to a second group. For ethical reasons, and because it was suspected that knowledge of vaccine administration would affect subsequent diagnoses, the experiment was conducted in a doubleblind fashion. That is, neither the subjects nor the administrators knew who received the vaccine and who received the placebo. The actual data for this experiment are as follows: Placebo group: n Vaccine group: n 201,299: 110 cases of polio observed 200,745: 33 cases of polio observed

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(a) Use a hypothesis-testing procedure to determine if the proportion of children in the two groups who contracted paralytic polio is statistically different. Use a probability of a type I error equal to 0.05. (b) Repeat part (a) using a probability of a type I error equal to 0.01. (c) Compare your conclusions from parts (a) and (b) and explain why they are the same or different. 10-74. Consider Supplemental Exercise 10-72. Suppose that prior to collecting the data, you decide that you want the error in estimating 1 x2 to be less than 1.5 psi. Specify the 2 by x1 sample size for the following percentage con dence: (a) 90% (b) 98% (c) Comment on the effect of increasing the percentage con dence on the sample size needed. (d) Repeat parts (a) (c) with an error of less than 0.75 psi instead of 1.5 psi. (e) Comment on the effect of decreasing the error on the sample size needed. 10-75. A random sample of 1500 residential telephones in Phoenix in 1990 found that 387 of the numbers were unlisted.

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A random sample in the same year of 1200 telephones in Scottsdale found that 310 were unlisted. (a) Find a 95% con dence interval on the difference in the two proportions and use this con dence interval to determine if there is a statistically signi cant difference in proportions of unlisted numbers between the two cities. (b) Find a 90% con dence interval on the difference in the two proportions and use this con dence interval to determine if there is a statistically signi cant difference in proportions of unlisted numbers between the two cities. (c) Suppose that all the numbers in the problem description were doubled. That is, 774 residents out of 3000 sampled in Phoenix and 620 residents out of 2400 in Scottsdale had unlisted phone numbers. Repeat parts (a) and (b) and comment on the effect of increasing the sample size without changing the proportions on your results. 10-76. In a random sample of 200 Phoenix residents who drive a domestic car, 165 reported wearing their seat belt regularly, while another sample of 250 Phoenix residents who drive a foreign car revealed 198 who regularly wore their seat belt. (a) Perform a hypothesis-testing procedure to determine if there is a statistically signi cant difference in seat belt usage between domestic and foreign car drivers. Set your probability of a type I error to 0.05. (b) Perform a hypothesis-testing procedure to determine if there is a statistically signi cant difference in seat belt usage between domestic and foreign car drivers. Set your probability of a type I error to 0.1. (c) Compare your answers for parts (a) and (b) and explain why they are the same or different. (d) Suppose that all the numbers in the problem description were doubled. That is, in a random sample of 400 Phoenix residents who drive a domestic car, 330 reported wearing their seat belt regularly, while another sample of 500 Phoenix residents who drive a foreign car revealed 396 who regularly wore their seat belt. Repeat parts (a) and (b) and comment on the effect of increasing the sample size without changing the proportions on your results. 10-77. Consider the previous exercise, which summarized data collected from drivers about their seat belt usage. (a) Do you think there is a reason not to believe these data Explain your answer. (b) Is it reasonable to use the hypothesis-testing results from the previous problem to draw an inference about the difference in proportion of seat belt usage (i) of the spouses of these drivers of domestic and foreign cars Explain your answer. (ii) of the children of these drivers of domestic and foreign cars Explain your answer. (iii) of all drivers of domestic and foreign cars Explain your answer. (iv) of all drivers of domestic and foreign trucks Explain your answer.

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