Homework 5 - Due Apr. 21, 2024 (Sunday) 11:59 pm Total score of this homework is 20 pt. - each of the sub-problems is for 1.25 pt. 1. An auditor for a government agency was assigned the task of evaluating reimbursement for office visits to physicians paid by Medicare. The audit was conducted on a sample of 75 reimbursements, with the following results: In 12 of the office visits, there was an incorrect amount of reimbursement. The amount of reimbursement was X = $93.70, S = $34.55. (a) At the 0.05 level of significance, is there evidence that the population mean reimbursement was less than $100? (b) At the 0.05 level of significance, is there evidence that the proportion of incorrect reimbursements in the population was greater than 0.10? (c) Discuss the underlying assumptions of the test used in (a). (d) What is your answer to (a) if the sample mean equals $90? (e) What is your answer to (b) if 15 office visits had incorrect reimbursements? Introduction to Business Analytics (33:136:287) Spring 2024 Instructor: Yifan Xie 2. Two methods of Natrella's research in 1963, A and B, were used in a determination of the latent heat of fusion of ice. The investigator wanted to find out by how much the methods differed. The data (TwoMethods.xlsx) give the change in total heat from ice at -0.72 to wafer 0 in calories per gram of mass. (a) Compute the pooled variance of the two sample. (b) Assuming that the population variances are equal, is there evidence of a difference in calories per gram of mass between the two methods at a 0.10 significance level? (c) Obtain the confidence interval of the average difference between the two methods at a 90% confidence level, and make a statistical decision based on the interval. 3. The data set (Concrete.xlsx) contains the compressive strength, in thousands of pounds per square inch (psi), of 40 samples of concrete taken two and seven days after pouring. (a) At the 0.01 level of significance, is there evidence of a difference in the mean strengths at two days and at seven days? (b) Find the p-value of the test in (a) and interpret its meaning. (c) At the 0.01 level of significance, is there evidence that the mean strength is lower at two days than at seven days? (d) Find the p-value of the test in (c) and interpret its meaning. A B 79.98 80.02 80.04 79.94 80.02 79.98 80.04 79.97 80.03 79.97 80.03 80.03 80.04 79.95 79.97 79.97 80.05 80.03 80.02 80.00 80.02 t-Test: Two-Sample Assuming Equal Variances Mean Variance Observations Pooled Variance Hypothesized Mean Difference t-Test: Two-Sample Assuming Equal Variances Input Variable 1 Range: $A$2:$A$14 Variable 2 Range: $B$2:$B$9 Hypothesized Mean Difference: 0 Labels 8 Alpha: 0.1 Output options $H$8 Output Range: New Worksheet Ply: New Workbook Variable 1 Variable 2 80.02076923 0.000574359 79.97875 0.000983929 13 0.000725253 0 19 3.472244847 0.001275502 df t Stat P(T Sample Two Days Seven Days t-Test: Paired Two Sample for Means 1 2.830 3.505 2 3.295 3.430 Input 3 2.710 3.670 Variable 1 Range: $B$2:$B$41 OK Cancel 4 2.855 3.355 Variable 2 Range: $C$2:$C$41 5 2.980 3.985 Hypothesized Mean Difference: 6 3.065 3.630 7 3.765 Labels 4.570 8 3.265 3.700 Alpha: 0.01 9 3.170 3.660 Output options 10 2.895 3.250 11 2.630 Output Range: $H$17 2.850 New Worksheet Ply: 12 2.830 3.340 New Workbook 13 2.935 3.630 14 3.115 3.675 15 2.985 3.475 16 3.135 3.605 t-Test: Paired Two Sample for Means 17 2.750 3.250 18 3.205 3.540 19 3.000 4.005 Mean 20 3.035 3.595 21 1.635 2.275 Variance Observations 22 1.765 3.415 23 2.045 3.225 24 2.670 3.790 25 1.355 4.575 26 1.425 4.070 27 3.875 5.100 28 3.020 3.205 29 2.290 4.260 t Stat P(T