Due Thursday, October 20th STAT 4202 HW 3 1. Let be a random sample from a distribution. Then, if and . a. Consider the interval estimator of of the form where and are constants. i. Given the relationship between and explain why an interval of this form is plausible. ii. Find iii. Show that if iv. Show that if and the pre-sampling coverage probability is and . the pre-sampling coverage probability is . v. Which of the intervals above is more precise? Why? b. Consider the interval estimator of of the form where and are constants. i. Given the relationship between and explain why an interval of this form is plausible. ii. Find iii. Find What does this say about this form of an interval estimator in this case? 2. Doritos sells 15.5 oz bags of chips. The bags are filled by machine and the actual weight of the chips in the bag varies from bag to bag. Suppose that the machines are set so the weight of the chips in a 15.5 oz bag is normally distributed with an average weight of 15.1 oz and 95% of all such bags have a weight between 14.806 and 15.394 oz. It is important to the company that both the average fill weight and the variability of the fill weights is controlled. As part of the quality control process in the plant, 77 bags were randomly removed from two different fill lines to be inspected. The bags were opened and the weight of the chips within was recorded. The data are summarized in the table below. Use the methods of chapter 11 to answer the following questions at the following confidence levels: a, c, e - 95%; b, d, f - 98%. In all cases, briefly explain why the answer is yes or no and if it's yes then explain the implication in terms of the problem. Line 1 Line 2 Average 15.1111 15.1626 Standard Deviation 0.1460 0.2097 Sample Size 41 36 Number defective (weight outside (14.806,15.394)) 3 5 a. b. c. d. e. f. Is there evidence the average fill weight is not 15.1 oz? Is there evidence of a difference in average fill weights between the two lines? Is there evidence the fill process is more variable than it should be? Is there evidence of a difference in the variability of the fill processes of the two lines? Is there evidence the process has an unacceptable rate of defective bags? Is there evidence of a difference in the rate of defective bags between the two lines