Please give me a full explain for the following question. Thank you. A local college cafeteria has a self-service soft ice cream machine. The cafeteria provides bowls that can hold up to 16 ounces of ice cream. The food service manager is interested in comparing the average amount of ice cream dispensed by male students to the average amount dispensed by female students. A measurement device was placed on the ice cream machine to determine the amounts dispensed. Random samples of 85 male and 78 female students who got ice cream were selected. The sample averages were 7.23 and 6.49 ounces for the male and female students, respectively. Assume that the population standard deviations are 1.22 and 1.17 ounces, respectively. 1. Let 1 and 2 be the population means of ice cream amounts dispensed by all male and all female students at this college, respectively. (a) Find the sampling distribution of the point estimator of 31 22. (b) Let Z denote the standardized point estimator of 3122. Calculate P (Z_0.005 Z Z_0.005), where Z_0.005 denotes the 0.005-critical value of Z. (c) Use b) to construct a (1 )% confidence interval for 3₁ 2₂. 2. (a) Using the significance level from 1-c), can you conclude that the average amount of ice cream dispensed by all male college students is larger than the average amount dispensed by all female college students? (b) Find the rejection and non-rejection regions of this hypothesis testing problem in terms of actual sample data. (c) What is the -error of this test if the true difference in mean ice cream amounts is 0.562 ounces?