8. [12 points] A manufacturer of power tools wants to estimate the average repair cost per...

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8. [12 points] A manufacturer of power tools wants to estimate the average repair cost per month for the power tools he sold to building contractors. He cannot obtain a repair cost for each power tool, but he can obtain the total amount spent for power tool repairs and the number of power tools owned by each contractor. Therefore, he decides to use cluster sampling, with each building contractor as cluster. The manufacturer selects a simple random sample of n = 20 from the N = 96 contractors he does businesses with. The data on total cost of repairs per contractor and number of power tools per contractor are given in the accompanying table. a. [3] Estimate the average repair cost per saw for the past month, and place a bound on the error of estimation using a 95% confidence level. b. [3] After checking his sales records, the manufacturer finds that he sold a total of 710 power tools to the contractors. Using this additional information, estimate the total amount spent on power tools repairs by these contractors and place a bound on the error of estimation using a 95% confidence level. c. [3] Suppose the manufacturer did not know the total number of power tools sold, estimate the total amount spent by the 96 contractors on power tools repairs. Place a bound on the error of estimation using a 95% confidence level. d. [3] The same manufacturer wants to estimate the average repair cost per power tool for the following month. How many clusters should he select for his sample if he wants the bound on the error of estimation to be less than $2? Building contractor Number of Power Tools 1 Total repair cost for Past month (dollars) 234569. 7 8 9 10 11 12 13 14 15 16 17 18 371122135000632-426 50 110 230 9 140 60 280 240 45 60 9 230 8 140 130 70 50 10 60 280 150 19 20 Total 5 8 130 110 120 2565 (Note: For the variance estimation calculations you may use S=845.5789; s = 6,908.6184). 8. [12 points] A manufacturer of power tools wants to estimate the average repair cost per month for the power tools he sold to building contractors. He cannot obtain a repair cost for each power tool, but he can obtain the total amount spent for power tool repairs and the number of power tools owned by each contractor. Therefore, he decides to use cluster sampling, with each building contractor as cluster. The manufacturer selects a simple random sample of n = 20 from the N = 96 contractors he does businesses with. The data on total cost of repairs per contractor and number of power tools per contractor are given in the accompanying table. a. [3] Estimate the average repair cost per saw for the past month, and place a bound on the error of estimation using a 95% confidence level. b. [3] After checking his sales records, the manufacturer finds that he sold a total of 710 power tools to the contractors. Using this additional information, estimate the total amount spent on power tools repairs by these contractors and place a bound on the error of estimation using a 95% confidence level. c. [3] Suppose the manufacturer did not know the total number of power tools sold, estimate the total amount spent by the 96 contractors on power tools repairs. Place a bound on the error of estimation using a 95% confidence level. d. [3] The same manufacturer wants to estimate the average repair cost per power tool for the following month. How many clusters should he select for his sample if he wants the bound on the error of estimation to be less than $2? Building contractor Number of Power Tools 1 Total repair cost for Past month (dollars) 234569. 7 8 9 10 11 12 13 14 15 16 17 18 371122135000632-426 50 110 230 9 140 60 280 240 45 60 9 230 8 140 130 70 50 10 60 280 150 19 20 Total 5 8 130 110 120 2565 (Note: For the variance estimation calculations you may use S=845.5789; s = 6,908.6184).