## Related questions with answers

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 (currently 75.7), studies show its shares have a good chance of outperforming the broad stock market in the long run” (Business- Week, March 2, 2009). The following satisfaction scores of three companies for the 4th quarters of 2007 and 2008 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 standard deviation can be assumed to equal 6 points in each case.

$\begin{matrix} \text{Company} & \text{2007 Score} & \text{2008 Score}\\ \text{Rite Aid} & \text{73} & \text{76}\\ \text{Expedia} & \text{75} & \text{77}\\ \text{J.C. Penney} & \text{77} & \text{78}\\ \end{matrix}$

a. For Rite Aid, is the increase in the satisfaction score from 2007 to 2008 statistically significant? Use $\alpha$= .05. What can you conclude? b. Can you conclude that the 2008 score for Rite Aid is above the national average of 75.7? Use $\alpha$= .05. c. For Expedia, is the increase from 2007 to 2008 statistically significant? Use $\alpha$= .05. d. When conducting a hypothesis test with the values given for the standard deviation, sample size, and α, how large must the increase from 2007 to 2008 be for it to be statistically significant? e. Use the result of part (d) to state whether the increase for J.C. Penney from 2007 to 2008 is statistically significant.

Solutions

VerifiedWe have given the research about how improving customer service affects stock prices for companies, whether stock prices rise or not. The research was done for three companies, Rite Aid, Expedia, and J.C. Penney.

This task's objective is to determine whether Rite Aid's increase in satisfaction from Year $1$ to Year $2$ is statistically significant, based on the following data:

- the sample size of Rite Aid of $n=60$,
- the population mean score at Year $1$ of $\bar x_1=73$,
- the population mean score at Year $2$ of $\bar x_2=76$,
- the standard deviation of Year $1$ of $\sigma_1=6$,
- the standard deviation of Year $2$ of $\sigma_2=6$,
- the level of significance of $\alpha=0.05$.

Let Sample 1 represent 2007 score and Sample 2 represent 2008 score.

- $\overline{x}_1$ = Sample mean = 73
- $\sigma_1$ = Population standard deviation = 6
- $n_1$ = Sample size = 60
- $\overline{x}_2$ = Sample mean = 76
- $\sigma_2$ = Population standard deviation = 6
- $n_2$ = Sample size = 60
- $\alpha$ = Significance level = 0.01

In this exercise, we determine the conclusion of a hypothesis test about a difference in two population means when the population standard deviations $\sigma_1$ and $\sigma_2$ are known.

*How do you execute a hypothesis test?*

We need to develop the hypotheses that can be used to test whether the mean year $1$ score is less than the mean year $2$ score. Then we need to find the $p$-value for these hypotheses and make a conclusion using the level of significance of $\alpha=0.05$. Researchers work to reject the null hypothesis and they develop the alternative hypothesis in which they believe that it explains a behavior. Denote the mean year $1$ score with $\mu_1$ and mean year $2$ score with Houston with $\mu_2$. We are given the standard deviations $\sigma_1=6$ and $\sigma_2=6$.

*Will the hypotheses be for a one-tailed or a two-tailed test?*

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