Question

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 350 customers selected from Supermarket I produced a mean satisfaction index of 7.9 (on a scale of 1 to 10, 1 being the lowest and 10 being the highest) with a standard deviation of 0.82. Another sample of 380 customers selected from Supermarket II produced a mean satisfaction index of 8.3 with a standard deviation of 0.33. Assume that the customer satisfaction index for each supermarket has an unknown and different population standard deviation.

Construct a 98% confidence interval for the difference between the mean satisfaction indexes for all customers for the two supermarkets.

Let μ1 be the mean satisfaction index for Supermarket I and μ2 be the mean satisfaction index for Supermarket II.

Round your answers to two decimal places.

<μ1-μ2<

Answer 1

A confidence interval, when te population standard deviation is not similar, is:

Since the sample sizes of both the samples are greater than 30, hence, normal distribution is used.

Here,

The two tailed critical value of the standard normal distribution is 2.33 at a significance level of 0.02.

Substituting the values given in the problem:

Thus, the required 98% confidence interval is