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where 1 is the mean absorption time of the competitive product and 2 is the mean absorption time of the new product. Assuming that the variances 2 and 2 are known, develop a 1 2 procedure for testing this hypothesis. 10-81. Suppose that we are testing H0: 1 2 versus H1: 1 2, and we plan to use equal sample sizes from the two populations. Both populations are assumed to be normal with unknown but equal variances. If we use 0.05 and if the true mean 1 , what sample size must be used for the 2 power of this test to be at least 0.90 10-82. Consider the re- ghting foam expanding agents investigated in Exercise 10-18, in which ve observations of each agent were recorded. Suppose that, if agent 1 produces a mean expansion that differs from the mean expansion of agent 1 by 1.5, we would like to reject the null hypothesis with probability at least 0.95. (a) What sample size is required (b) Do you think that the original sample size in Exercise 10-18 was appropriate to detect this difference Explain your answer. 10-83. A fuel-economy study was conducted for two German automobiles, Mercedes and Volkswagen. One vehicle of each brand was selected, and the mileage performance was observed for 10 tanks of fuel in each car. The data are as follows (in miles per gallon): Mercedes 24.7 24.8 24.9 24.7 24.5 24.9 24.6 23.9 24.9 24.8 Volkswagen 41.7 42.3 41.6 39.5 41.9 42.8 42.4 39.9 40.8 29.6

on norms for ages 17 0 through 17 3 (standard scores are banded by 90% confidence interval).

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(a) Construct a normal probability plot of each of the data sets. Based on these plots, is it reasonable to assume that they are each drawn from a normal population (b) Suppose that it was determined that the lowest observation of the Mercedes data was erroneously recorded and should be 24.6. Furthermore, the lowest observation of the Volkswagen data was also mistaken and should be 39.6. Again construct normal probability plots of each of the data sets with the corrected values. Based on these new plots, is it reasonable to assume that they are each drawn from a normal population (c) Compare your answers from parts (a) and (b) and comment on the effect of these mistaken observations on the normality assumption. (d) Using the corrected data from part (b) and a 95% con dence interval, is there evidence to support the claim that the variability in mileage performance is greater for a Volkswagen than for a Mercedes 10-84. Reconsider the fuel-economy study in Supplemental Exercise 10-83. Rework part (d) of this problem using an appropriate hypothesis-testing procedure. Did you get the same answer as you did originally Why 10-85. An experiment was conducted to compare the lling capability of packaging equipment at two different wineries. Ten bottles of pinot noir from Ridgecrest Vineyards were randomly selected and measured, along with 10 bottles of pinot noir from Valley View Vineyards. The data are as follows ( ll volume is in milliliters): Ridgecrest 755 753 752 751 753 751 752 753 753 754 756 755 755 Valley View 754 756 756 757 756 756 755

Peabody Picture Vocabulary Test-Revised (PPVT-R) Vineland Adaptive Behavior Scales (Expanded Form) Wechsler Adult Intelligence Test-Revised (WAIS-R) Test Results and Interpretation In contrast to the 36-point Verbal deficit that Chester displayed on the WISC-R at age 14 (P-IQ = 101, V-IQ = 65), he performed at a normal level of functioning on both WAIS-R scales at the present evaluation His WAIS-R Performance IQ of 113 9 (High Average intelligence, 81st percentile) was still a significant 24 points greater than his Verbal IQ; further, differences as large as 24 points are abnormal, occurring less than 5% of the time in adolescents or adults with average intelligence Yet his WAIS-R Verbal IQ of 89 5 (23rd percentile) placed him at the juncture of the Low Average and Average categories, not within the deficient range of mental ability.

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(a) What assumptions are necessary to perform a hypothesistesting procedure for equality of means of these data Check these assumptions. (b) Perform the appropriate hypothesis-testing procedure to determine whether the data support the claim that both wineries will ll bottles to the same mean volume. 10-86. Consider Supplemental Exercise 10-85. Suppose that the true difference in mean ll volume is as much as 2 uid ounces; did the sample sizes of 10 from each vineyard provide good detection capability when 0.05 Explain your answer. 10-87. A Rockwell hardness-testing machine presses a tip into a test coupon and uses the depth of the resulting depression to indicate hardness. Two different tips are being compared to determine whether they provide the same Rockwell C-scale hardness readings. Nine coupons are tested, with both tips being tested on each coupon. The data are shown in the accompanying table.

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