Quadro Corporation has two supermarket stores in a city. The company’s quality control department wanted to check if the customers are equally satisfied with the service provided at these two stores. A sample of 380 customers selected from Supermarket I produced a mean satisfaction index of 7.6 (on a scale of 1 to 10, 1 being the lowest and 10 being the highest) with a standard deviation of .75. Another sample of 370 customers selected from Supermarket II produced a mean satisfaction index of 8.1 with a standard deviation of .59. Assume that the customer satisfaction index for each supermarket has unknown but same population standard deviation.
a. Construct a 98% confidence interval for the difference between the mean satisfaction indexes for all customers for the two supermarkets.
b. Test at a 1% significance level whether the mean satisfaction indexes for all customers for the two supermarkets are different.