{b} Perform the twosample ttest 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, i1 - i2. Let sample 1 oorrespend to the old plant and sample 2 correspond to the new plant. x1 - i2 = (Round to three decimal planes as needed J- Determine the two-sample t-statistic. t= (Round to three decimal places as needed.)Ideniify the pvalue. pvalue = [Round to three decimal places as needed.) Determine the conclusion for this test. The p-value is O, 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.) The interaction in the model statistically significant, meaning that the two plants different average costs per unit. The average cost per unit for the old plant the average cost per unit for the new plant.{d} Compare the results from parts (b) and {a}. Do they agree?l You should take into account the precision of the estimates and your answer to part {a}. Part (b1 indicates that there is l1 evidenee that there is a difference in the average cost per unit, while part (6) indicates that the two plants |:l different average costs per unit. Therefore, the results |:l (e) Does the estimated multiple regression used in the analysis of covariance meet the similar variances condition? O A. Yes; there is insufficient evidence that the variances for the two plants are different. O B. No; the residuals for the old plant vary more than the residuals for the new plant. O C. No; the residuals for the new plant vary more than the residuals for the old plant. O D. Yes; the variance for the average cost per unit are less than 1 for each plant.= Homework: HW CH25 Question 4, 25.1.42-T HW Score: 17.63%, 1.41 of 8 points O Part 1 of 8 Points: 0.79 of 1 Save 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? O A. 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. O B. 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. O C. 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. O D. 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.X Data table Average Cost Material Cost Plant Plant Dummy Plant Dummy x Material Cost ($/unit) ($/unit) 38.18 0.9625 New 0.9625 37.62 3.8441 Old 0 0 37.83 1.9218 New 1.9218 43.86 2.2378 Old 0 0 40.84 2.4333 New 2.4333 57.42 7.0793 Old 0 0 38.52 3.1816 New 3.1816 55.01 5.3308 Old 0 0 43.78 3.8853 New 3.8853 28.32 0.7051 Old - 0 - 0 41.81 4.3282 New 4.3282 48.16 5.5889 Old 0 0 45.26 5.4203 New 5.4203 43.24 2.2285 Old 0 0 48.99 6.0157 New 6.0157 33.21 0.7116 Old 0 0 46.04 6.1913 New 6.1913 38.54 3.7235 Old 0 53.11 7.0067 New 7.0067 38.67 2.0903 Old 0 0