NOTE: Point values are listed next to each problem. NOTE: The data has been saved in a Minitab project named asmt7 s21 miniproj.mpx which is located under DataFiles. Deepak and Dylan manufacture paper bags and want to improve the tensile strength of their paper bags. They suspect that changing the concentration (percentage) of hardwood in the paper bag will change the tensile strength. They decide to test three levels of hardwood concentrations (percentages): 10%, 15% and 20%. They take a random sample of 9 bags from each of the concentration levels and measure the tensile strength (pounds per square inch) of each bag. The results were entered in a Minitab worksheet for analysis. Note: To save space the data has been listed in rows on this document. The three percentages represent columns in the Minitab project. 10% 16 17 15 16 18 16 16 15 17 15% 16 18 19 17 16 18 16 18 19 20% 18 20 20 19 18 19 17 19 16 Let Mi = true average tensile strength for hardwood concentration (percentage) i = 1 (10%), 2 (15%), 3 (20%) 1. Perform the appropriate test to determine whether can one conclude that at least one of the hardwood concen- rations (percentages) yields a significantly different paper bag tensile strength, on the average. Use a = 0.05. Be sure to include all the steps in your hypothesis test!) (6 pts) 2. If appropriate, use Tukey's test and the grouping method to determine which concentration(s) is/are signif- icantly different with respect to mean paper bag tensile strength. (Be sure to justify your conclusions!) (If you did not conclude a significant difference in mean paper bag tensile strength in Question 1, just state that.) (3 pts) 3. If appropriate, use Tukey's test and the confidence interval method to determine which concentration(s) is/are significantly different with respect to mean paper bag tensile strength. (Be sure to justify your conclu sions!) (If you did not conclude a significant difference in mean paper bag tensile strength in Question 1, just state that .) (3 pts) 4. If appropriate, use Tukey's test and the p-value method to determine which concentration(s) is/are signifi- cantly different with respect to mean paper bag tensile strength. (Be sure to justify your conclusions!) (If you did not conclude a significant difference in mean paper bag tensile strength in Question 1, just state that.) (3 pts)QUESTION 1 Deepak and Dylan manufacture paper bags and want to improve the tensile strength of their paper bags. They suspect that changing the concentration (percentage) of hardwood in the paper bag will change the tensile strength. They decide to test three levels of hardwood concentrations (percentages): 10%, 15% and 20%. They take a random sample of 9 bags from each ofthe concentration levels and measure the tensile strength (pounds per square inch) of each bag. The results were entered in a Minitab worksheet for analysis. Let mu_i = true average tensile strength of concentration i = 1 (10%), 2 (15%}, 3 (20%) What is the appropriate null hypothesis? 0 a. H_O: mu_1 = mu_2 = mu_a (One can conclude a significant difference in average tensile strength between the three concentrations.) b. H_O: mu_'l = mu_2 = mu_a (One cannot conclude a significant difference in mean tensile strength between the three concentrations) c. H_a: mu_l = mu_2 = mu_3 (One cannot conclude a signicant difference in mean tensile strength between the three concentrations) d. None of the above. QUESTION 2 Deepak and Dylan manufacture paper bags and want to improve the tensile strength of their paper bags. They suspect that changing the concentration (percentage) of hardwood in the paper bag will change the tensile strength. They decide to test three levels of hardwood concentrations (percentages): 10%. 15% and 20%. They take a random sample of 9 bags from each of the concentration levels and measure the tensile strength (pounds per square inch) of each bag. The resuhss were entered in a Minitab worksheet for analysis. Let mu_i = true average tensile strength of concentration i = 1 (10%), 2 (15%), 3 (20%) What is the appropriate alternate hypothesis? a. H_a: mu_l not: mu_2 not: mu_3. (at least one of theconcentrations yields a signicantly different average tensile strength) b. H_a: at least one of the mu_i's is different. (at least one of the concentrations yields a significamly different average tensile strength) c. H_a: mu_l = mu_2 = mu_3 (cannot conclude a signicant difference in average tensile strength between the three concentrations) d. None of the above. QUESTION 3 Deepak and Dylan manufacture paper bags and want to improve the tensile strength of their paper bags. They suspect that changing the concentration (percentage) of hardwood in the paper bag will change the tensile strength. They decide to test three levels of hardwood concentrations (percentages): 10%, 15% and 20%. They take a random sample of 9 bags from each ofthe concentration levels and measure the tensile strength (pounds per square inch) of each bag. The results were entered in a Minitab worksheet for analysis. Let mu_i = true average tensile strength of concentration i = 1 (10%). 2 (15%), 3 (20%) What is the appropriate p-value? (exactly as reported in the Minitab output) 0.0024 QUESTION 4 QUESTION 4 Deepak and Dylan manufacture paper bags and want to improve the tensile strength of their paper bags. They suspect that changing the concentration (percentage) of hardwood in the paper bag will change the tensile strength. They decide to test three levels of hardwood concentrations (percentages): 10%, 15% and 20%. They take a random sample of 9 bags from each of the concentration levels and measure the tensile strength (pounds per square inch) of each bag. The results were entered in a Minitab worksheet for analysis. Let mu_i = true average tensile strength of concentration i = 1 (10%), 2 (15%), 3 (20%) What is the appropriate rejection region? o a. Reject H_0 if p-value alpha = 0.05 C. Reject H_0 if z > 1.645 d. None of the above. QUESTION 5 Deepak and Dylan manufacture paper bags and want to improve the tensile strength of their paper bags. They suspect that changing the concentration (percentage) of hardwood in the paper bag will change the tensile strength. They decide to test three levels of hardwood concentrations (percentages): 10%, 15% and 20%. They take a random sample of 9 bags from each of the concentration levels and measure the tensile strength (pounds per square inch) of each bag. The results were entered in a Minitab worksheet for analysis. Let mu_i = true average tensile strength of concentration i = 1 (10%), 2 (15%), 3 (20%) What is the appropriate conclusion? Since the p-value > alpha = 0.05, reject H_0 and conclude that at least one of the concentrations yields a significantly different a average tensile strength. ob. Since the p-value