Question

1. Assume that you have recently been hired by the audit department of the Iowa State Tax Commission. The chairman of the audit department is interested in estimating the mean tax collected per transaction at a local home improvement center. The chairman asks that you conduct an audit for the home improvement center and develop an estimate for the mean tax collected per transaction by developing a 95% confidence interval estimate for the population mean. You define this normally distributed population as the individual sales tax payments made by customers at the home improvement center in a given week. You take a random sample of 20 transactions with the following data: $0.44 -$0.36 $1.20 $0.43 $1.00 $1.47 $0.83 $0.50 $3.34 $1.58 $1.46 $1.10 $2.60 $0.00 $1.12 -$1.70 $0.83 $1.99 $0.77 $1.34 Manually calculate the mean and standard deviation from this sample and then manually construct a 95% confidence interval for the mean tax collected per transaction along with the interpretation of your results. Show your formulas and calculations for the mean, standard deviation, and 95% confidence interval along with your interpretation of the confidence interval result on a separate page. (10 points)

Answer 1

044 -0.447 | 0.1998 12 0313 | 0.0980 043 -0.457] 0.2088 10.113 | 0.0128 1.47 0.583 | 0.3399 0.83 -0.0571 0.0032 05-0387| 0.1498 3.342.453 | 6.0172 1.58 0.693 | 0.4802 1.46 0.573| -0.36-1.247| 1.5550 در سراسر 1 . 1۔ |1987- 3 . 9482 || ایرای 2.6 1.713 | 29344 0 -0.887 0.7868 1.12 0.233 | 0.0543 ۔ 1 . 7 2 . 587- | 6 . 6926 0.83 -0.057 | 0.0032 199 1.103 | 12166 0.77 -0.117| 0.0137 134 0453 | 02052 17.74 25.2480 ی

Sample mean x = $x = 13,74 = 0.8870 n 20 W Standard deviation s= . (x-x)2 _ 25.2480 = 1.1528 V n-1 V20-1 95% confidence interval is = x t* Critical t = 2.093 95% confidence interval is = Ž * - = 0.8870 + 2.093* 1.1528 V20 =0.8870+ 0.5395 =(0.3475 , 1.4265) 95% confidence that the true proportion is fall between 0.3475 and 1.4265