1. ( 24 points) To compare customer satisfaction levels of two competing cable television companies, 174 customers of Company 1 and 355 customers of Company 2 were randomly selected and were asked to rate their cable companies on a five-point scale, with 1 being least satisfied and 5 most satisfied. The survey results are summarized in the following table: Company 1 Company 2 n1 = 174 n2 = 355 X1 = 3.51 X2 = 3.24 $1 = 0.51 $2 = 0.52 (a) (6 points) Construct a point estimate and a 99% confidence interval for /1 - /2, the difference in average satisfaction levels of customers of the two companies as measured on this five-point scale. (b) (3 points) Interpret the confidence interval based on the problem. (c) (10 points) Test at the 1% level of significance whether the data provide sufficient evidence to conclude that Company 1 has a higher mean satisfaction rating than does Company 2. Use the critical value approach. Make sure you right the null and alternative hypothesis before proceeding. (d) (5 points) Compute the p-value for the hypothesis in part (c) and make your conclusion using a = 0.01