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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 efficacy 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 subse- quent diagnoses, the experiment was conducted in a double- blind 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 = 201,299: 110 cases of polio observed Vaccine group: n = 200,745: 33 cases of polio observed (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 ex- plain why they are the same or different.10-51. Consider the foam data in Exercise 10-18. Construc the following: (a) A 90% two-sided confidence interval on of/o. (b) A 95% two-sided confidence interval on of/of. Commen on the comparison of the width of this interval with th width of the interval in part (a). (c) A 90% lower-confidence bound on a /U 2 10-52. Consider the film speed data in Exercise 10-24. Tes10-21. In semiconductor manufacturing, wet chemical etch- ing is often used to remove silicon from the backs of wafers prior to metalization. The etch rate is an important characteris- tie in this process and known to follow a normal distribution. Two different etching solutions have been compared, using two random samples of 10 wafers for each solution, The observed etch rates are as follows (in mils per minute): Solution 1 Solution 2 9.9 10.6 10.2 10.0 9.4 10.3 10.6 10.2 9.3 10.0 10.7 10.7 9.6 10.3 10.4 10.4 10.2 10.1 10.5 10.310-11. The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of cata- lyst used in the process. The standard deviation of active con- centration is known to be 3 grams per liter, regardless of the catalyst type. Ten observations on concentration are taken with each catalyst, and the data follow: Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2. 71.0 Catalyst 2: 66.4, 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.810-7. Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers, The variance of road octane number for formulation I is of = 1.5, and for Formulation 2 it is of = 1.2. Two random samples of size m = 15 and n, = 20 are tested, and the mean road octane numbers observed are x) = 89.6 and x, = 92.5. Assume normality. (a) Construct a 95% two-sided confidence interval on the difference in mean road octane number. (b) If formulation 2 produces a higher road octane number than formulation 1, the manufacturer would like to detect
