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 0.75. Another sample of 370 customers

selected from Supermarket II produced a mean satisfaction index of 8.1 with a standard

deviation of 0.59. 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 the 1% significance level whether the mean satisfaction indexes for all

customers for the two supermarkets are different.