Two machines are used for filling plastic bottles with a net volume of 16.0 oz. The fill volume can be assumed normal with, s1 = 0.02 and s2 = 0.025. A member of the quality engineering staff suspects that both machines fill to the same mean net volume, whether or not this volume is 16.0 oz. A random sample of 10 bottles is taken from the output of each machine with the following results:

(a) Do you think the engineer is correct? Use the p – value approach. (b) Find a 95% CI on the difference in means. Exercise 3 Two machine are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be s1= 0.01 and s2 = 0.15 fluid ounce for two machines, respectively. Two random samples of n1 = 12 bottles from machine 1 and n2=10 bottles from machine 2 are selected, and the sample mean fill volumes are 1 x =30.61 2x =30.24 fluid ounces. Assume normality. (i) Test the hypothesis that both machines fill to the same mean volume. Use the P-value approach; (ii) Construct a 90% two-sided CI on the mean difference in fill volume; and (iii) Construct a 95% two-sided CI on the mean difference in fill volume. Compare and comment on the width of this interval to the width of the interval in part (ii). Exercise 7 Professor A claims that a probability and statistics student can increase his or her score on tests if the person is provided with a pre-test the week before the exam. To test her theory she selected 16 probability and statistics students at random and gave these students a pre-test the week before an exam. She also selected an independent random sample of 12 students who were given the same exam but did not have access to the pre-test. The first group had a mean score of 79.4 with standard deviation 8.8. The second group had sample mean score 71.2 with standard deviation 7.9. (i) Do the data support Professor A claims that the mean score of students who get a pre-test are different from the mean score of those who do not get a pretest before an exam. Use the P-value approach and assume that their variances are not equal. (ii) Construct a 95% CI for the difference in mean score of students who get a pre-test and those who do not get a pre-test before an exam. Interpret this interval. Exercise 8 The rollover rate of sport utility vehicles is a transportation safety issue. Safety advocates claim that the manufacturer A’s vehicle has a higher rollover rate than that of manufacturer B. One hundreds crashes for each of this vehicles were examined. The rollover rates were pA=0.35 and pB=0.25. i) By using the P-value approach, does manufacturer A’s vehicle has a higher rollover rate than manufacturer B’s? (ii) Construct a 95% CI on the difference in the two rollover rates of the vehicle. Interpret this interval.