Question

When a company's satisfaction score has improved over the prior year's results and is above the national average (currently 75.7), studies show its shares have a good chance of outperforming the broad stock market in the long run. The following satisfaction scores of three companies for the 4th quarters of two previous years were obtained from the American Customer Satisfaction Index. Assume that the scores are based on a poll of 60 customers from each company. Because the polling has been done for several years, the population standard deviation can be assumed to equal 7 points in each case.

Company Year 1 Score Year 2 Score
Rite Aid 74 76
Expedia 74 75
J.C. Penney 75 78

a. For Rite Aid, is the increase in the satisfaction score from Year 1 to Year 2 statistically significant? Use α = .05 and null hypothesis is H0: μ1 - μ2 ≤ 0. What can you conclude? (Hint: μ1 represents Year 2 population mean score. This can be deduced from H0.)

Z-value: ________ (Numeric Answer, to 2 decimals)
Critical Z: ________ (Numeric Answer, to 3 decimals)
The difference ________ (Word Answer) statistically significant.

b. Can you conclude that the Year 2 score for Rite Aid is above the national average of 75.7? Use α = .05 and null hypothesis is H0: μ ≤ 75.7. Enter negative value as negative number.

Z-value: ________ (Numeric Answer, to 2 decimals)
Critical Z: ________ (Numeric Answer, to 3 decimals)
We ________ (Word Answer) that customer service has improved for Rite Aid.

c. For Expedia, is the

Answer 1

The increase in satisfaction score for Rite Aid from Year 1 to Year 2 is not statistically significant, and we cannot conclude that the Year 2 score is above the national average.

Step-by-step explanation:

Given the satisfaction scores for Rite Aid in Year 1 and Year 2 as 74 and 76 respectively, we can calculate whether the increase in satisfaction score is statistically significant or not.

The null hypothesis (H0) is that the population mean of Year 2 satisfaction scores is less than or equal to the population mean of Year 1 satisfaction scores.

By assuming a population standard deviation of 7, we can calculate the z-value to be 0.286 and the critical z-value to be -1.96 (for α=0.05).

Since the z-value is not less than the critical z-value, we fail to reject the null hypothesis. This means that the increase in satisfaction score from Year 1 to Year 2 for Rite Aid is not statistically significant.

We cannot conclude that the Year 2 satisfaction score for Rite Aid is above the national average of 75.7.

Therefore, we cannot say that customer service has improved for Rite Aid.