part c (only)

Problem 4 An industry is considering revision of its retirement policy and wants to estimate the proportion of employees that favor the new policy. The industry consists of 87 separate plants (cluster) located throughout the United States. Because results must be obtained quickly and with little cost, the industry decides to use cluster sampling with each plant as a cluster. A simple random sample of 15 plants is selected, and the opinions of the employees in these plants are obtained by questionnaire. The results are as shown in the accompanying table below. (a) Estimate the total number of employees in the industry who favor the new retirement policy and place a bound on the error of estimation. (b) Using the unbiased estimator of the average of the N plants (-), obtain the estimated total number of employees in the industry who favor the new retirement policy and place a bound on the error of estimation. (c) How many plants should be sampled for estimating the proportion of employees favoring the new retirement policy to have a bound of 0.08 on the error of estimation? Given that 0-0,452 Plant Number of employees Number favoring new policy 51 62 53 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 49 73 101 48 65 49 73 61 58 $2 65 49 55 40 45 63 31 38 30 54 45 51 29 46 37 42 Problem 4 An industry is considering revision of its retirement policy and wants to estimate the proportion of employees that favor the new policy. The industry consists of 87 separate plants (cluster) located throughout the United States. Because results must be obtained quickly and with little cost, the industry decides to use cluster sampling with each plant as a cluster. A simple random sample of 15 plants is selected, and the opinions of the employees in these plants are obtained by questionnaire. The results are as shown in the accompanying table below. (a) Estimate the total number of employees in the industry who favor the new retirement policy and place a bound on the error of estimation. (b) Using the unbiased estimator of the average of the N plants (-), obtain the estimated total number of employees in the industry who favor the new retirement policy and place a bound on the error of estimation. (c) How many plants should be sampled for estimating the proportion of employees favoring the new retirement policy to have a bound of 0.08 on the error of estimation? Given that 0-0,452 Plant Number of employees Number favoring new policy 51 62 53 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 49 73 101 48 65 49 73 61 58 $2 65 49 55 40 45 63 31 38 30 54 45 51 29 46 37 42