A college sorority is trying to decide which of two competing pizza chains to select for a sole-source pizza contract over the next five years. Agatha, the sorority president, claims that all pizza tastes the same, so the decision should be based purely on price. Several newer members disagree and feel that taste can indeed vary from pizza chain to pizza chain. Fortunately, the sorority has some recent pizza tastiness data available, in the form of the following summary data based on seven scores on a pizza tastiness scale of O through 20 for Chain A and a further seven scores on the same scale for Chain B: x^-A = 9.386x^-b = 14.029 SA = 3.044 Sb= 3.502 Assuming that the two samples of pizza tastiness scores can be treated as independent samples and that the population variance of pizza tastiness is equal across the two chains: a) Use an appropriate hypothesis test to see whether there appears to be a difference in pizza tastiness between the pizza from Chain A and the pizza from Chain B. Use a 5% significance level. b) Calculate a 90% confidence interval for the difference in mean pizza tastiness across the two chains. c) Repeat parts a) and b), but this time assume that the samples of pizza tastiness scores must be treated as being paired, rather than independent. (The mean paired difference, d, is -4.643 and the sample standard deviation for the paired differences, is 4.927)