A polymer is manufactured in a batch chemical process. Viscosity measurements are normally made on each batch, and long experience with the process indicated that the variability experience in the process is fairly stable with = 20. Fifteen batch viscosity measurements are given as follows: 720, 718, 780, 760, 750, 764, 756, 742, 745, 755, 749, 744, 745, 742, 795. A process change that involves switching the type of catalyst used in the process is made. Following the process change, each batch viscosity measurements are taken: 740, 780, 734, 750, 780, 763, 740, 770.Assume that the process variability is unaffected by the catalyst change. If the difference in mean batch viscosity is less than 11, the manufacture would like to detect it with a high probability. (a) Formulate and test appropriate hypothesis using = 0.10. What are your conclusions? Find P-value. (b) Find a 90% confidence interval on the difference in mean batch viscosity resulting from the process change. (c) Compare the results of parts (a) and (b) and discuss your findings. (d) What sample size would be required in each population if you wanted to be 95% confident that the error in estimating the difference in mean batch viscosity is less than 6.