| Average_Cost_($/unit) | Material_Cost_($/unit) | Plant | Plant_Dummy | Plant_Dummy*Material_Cost |
| 37.12 | 1.1776 | New | 1 | 1.1776 |
| 30.86 | 0.8591 | Old | 0 | 0 |
| 35.02 | 1.9581 | New | 1 | 1.9581 |
| 42.64 | 2.0733 | Old | 0 | 0 |
| 43.32 | 2.1698 | New | 1 | 2.1698 |
| 42.61 | 1.4286 | Old | 0 | 0 |
| 43.22 | 3.3642 | New | 1 | 3.3642 |
| 43.17 | 2.3238 | Old | 0 | 0 |
| 44.45 | 3.8187 | New | 1 | 3.8187 |
| 34.07 | 1.8369 | Old | 0 | 0 |
| 41.21 | 4.7357 | New | 1 | 4.7357 |
| 40.66 | 2.5069 | Old | 0 | 0 |
| 47.19 | 5.2377 | New | 1 | 5.2377 |
| 43.37 | 1.5158 | Old | 0 | 0 |
| 45.77 | 5.7391 | New | 1 | 5.7391 |
| 44.15 | 4.3596 | Old | 0 | 0 |
| 47.13 | 6.2888 | New | 1 | 6.2888 |
| 46.88 | 7.0486 | Old | 0 | 0 |
| 50.58 | 7.4823 | New | 1 | 7.4823 |
| 42.51 | 1.4827 | Old | 0 | 0 |
A company manufactures custom metal blanks. This analysis considers the factors that affect the cost to manufacture these blanks. The data, available below, were sampled from the accounting records of 20 previous orders filled during the last three months. The data measure performance at two plants, identified as "Old" and "New" in the column Plant. Complete parts (a) through (e) below. Click the icon to view the data table (a) Would it be appropriate for management to compare the two plants using a two-sample comparison of the costs per unit, or would such a comparison be confounded by different material costs per unit in the two plants? OA. A two-sample comparison would be appropriate. Since the mean cost and standard deviation are the same for each group (costs are paired between the two plants), material cost per unit cannot be a confounding variable. OB. A two-sample comparison would be appropriate. Since the cost is not related to the material cost per unit, machine use per unit cannot be a confounding variable. OC. A two-sample comparison would not be appropriate. Since the cost is related to the material cost per unit, machine use per unit is a confounding variable. OD. A two-sample comparison may not be appropriate. Since the mean cost and standard deviation differ for the two groups, machine use may be a confounding variable. (b) Perform the two-sample t-test to compare the average cost per unit at the two plants for a = 0.05. Summarize this analysis, assuming that there are no lurking variables. Find the sample statistic, X, -X. Let sample 1 correspond to the old plant and sample 2 correspond to the new plant. x1 - x2 = (Round to three decimal places as needed.) Determine the two-sample t-statistic. t(Round to three decimal places as needed.) Identify the p-value. p-value = (Round to three decimal places as needed.) Determine the conclusion for this test The p-value is VU, SO the null hypothesis. There is evidence to conclude that there is a difference in the average cost per unit at the two plants. (c) Compare the average cost per unit at the two plants using an analysis of covariance with a =0.05. Summarize the comparison based on this analysis. Represent these categories using a dummy variable coded as 1 if the plant is new. (Assume for the moment that the model meets the conditions for the MRM.) V statistically significant, meaning that the two plants different average costs per unit. The average cost per unit for the old plant The Interaction in the model cost per unit for the new plant. v the average (d) Compare the results from parts (b) and (c). Do they agree? You should take into account the precision of the estimates and your answer to part (a) evidence that there is a difference in the average cost per unit, while part (c) indicates that the two plants different average costs per unit. Therefore, the Part (b) indicates that there is results (e) Does the estimated multiple regression used in the analysis of covariance meet the similar variances condition? O A. Yes; the variance for the average cost per unit are less than 1 for each plant OB. No, the residuals for the new plant vary more than the residuals for the old plant. OC. No; the residuals for the old plant vary more than the residuals for the new plant. OD. Yes; there is insufficient evidence that the variances for the two plants are different. A company manufactures custom metal blanks. This analysis considers the factors that affect the cost to manufacture these blanks. The data, available below, were sampled from the accounting records of 20 previous orders filled during the last three months. The data measure performance at two plants, identified as "Old" and "New" in the column Plant. Complete parts (a) through (e) below. Click the icon to view the data table (a) Would it be appropriate for management to compare the two plants using a two-sample comparison of the costs per unit, or would such a comparison be confounded by different material costs per unit in the two plants? OA. A two-sample comparison would be appropriate. Since the mean cost and standard deviation are the same for each group (costs are paired between the two plants), material cost per unit cannot be a confounding variable. OB. A two-sample comparison would be appropriate. Since the cost is not related to the material cost per unit, machine use per unit cannot be a confounding variable. OC. A two-sample comparison would not be appropriate. Since the cost is related to the material cost per unit, machine use per unit is a confounding variable. OD. A two-sample comparison may not be appropriate. Since the mean cost and standard deviation differ for the two groups, machine use may be a confounding variable. (b) Perform the two-sample t-test to compare the average cost per unit at the two plants for a = 0.05. Summarize this analysis, assuming that there are no lurking variables. Find the sample statistic, X, -X. Let sample 1 correspond to the old plant and sample 2 correspond to the new plant. x1 - x2 = (Round to three decimal places as needed.) Determine the two-sample t-statistic. t(Round to three decimal places as needed.) Identify the p-value. p-value = (Round to three decimal places as needed.) Determine the conclusion for this test The p-value is VU, SO the null hypothesis. There is evidence to conclude that there is a difference in the average cost per unit at the two plants. (c) Compare the average cost per unit at the two plants using an analysis of covariance with a =0.05. Summarize the comparison based on this analysis. Represent these categories using a dummy variable coded as 1 if the plant is new. (Assume for the moment that the model meets the conditions for the MRM.) V statistically significant, meaning that the two plants different average costs per unit. The average cost per unit for the old plant The Interaction in the model cost per unit for the new plant. v the average (d) Compare the results from parts (b) and (c). Do they agree? You should take into account the precision of the estimates and your answer to part (a) evidence that there is a difference in the average cost per unit, while part (c) indicates that the two plants different average costs per unit. Therefore, the Part (b) indicates that there is results (e) Does the estimated multiple regression used in the analysis of covariance meet the similar variances condition? O A. Yes; the variance for the average cost per unit are less than 1 for each plant OB. No, the residuals for the new plant vary more than the residuals for the old plant. OC. No; the residuals for the old plant vary more than the residuals for the new plant. OD. Yes; there is insufficient evidence that the variances for the two plants are different
