Question

Will improving customer service result in higher stock prices for the companies providing the better service? "When a company's satisfaction score has improved over the prior year's results and is above the national average (75.5), 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 an economic indicator. Assume that the scores are based on a poll of 50 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 6 points in each case.

Company	Year 1	Year 2
Company A	73	76
Company B	74	77
Company C	77	78

For Company A, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use

α = 0.05.

(Let μ₁ = the satisfaction score for year 2 and μ₂ = the satisfaction score for year 1.)

Hypotheses:

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

1. Calculate the test statistic. (Round your answer to two decimal places.)

2. Calculate the p-value. (Round your answer to four decimal places.)

3. What is your conclusion?

A. Do not reject H₀. There is insufficient evidence to conclude that the customer service has improved for Company

B. Do not reject H₀. There is sufficient evidence to conclude that the customer service has improved for Company

C. Reject H₀. There is insufficient evidence to conclude that the customer service has improved for Company

D. Reject H₀. There is sufficient evidence to conclude that the customer service has improved for Company A.

4. Can you conclude that the year 2 score for Company A is above the national average of 75.5? Use α = 0.05

5. State the hypotheses.

6. Calculate the test statistic. (Round your answer to two decimal places.)

7, Calculate the p-value. (Round your answer to four decimal places.)

8. For Company B, is the increase from year 1 to year 2 statistically significant? Use α = 0.05. (Let μ₁ = the satisfaction score for year 2 and μ₂ = the satisfaction score for year 1.)

9. Calculate the test statistic. (Round your answer to two decimal places.)

10. Calculate the p-value. (Round your answer to four decimal places.)

11. When conducting a hypothesis test with the values given for the standard deviation, sample size, and α, how large must the increase from year 1 to year 2 be for it to be statistically significant? (Round your answer to two decimal places.)

Answer 1