As mentioned in Exercise 10.31, Quadro Corporation has two supermarkets 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 an unknown and different 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.
c. Suppose that the sample standard deviations were .88 and .39, respectively. Redo parts a and b. Discuss any changes in the results.