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." 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 55 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 7 points in each case. Company Year 1 Score Year 2 Score Rite Aid 72 75 Expedia 78 79 J.C. Penney 75 77
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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." 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 55 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 7 points in each case.
| Company | Year 1 Score | Year 2 Score |
| Rite Aid | 72 | 75 |
| Expedia | 78 | 79 |
| J.C. Penney | 75 | 77 |
a. For Rite Aid, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use ax=.05 and null hypothesis is H0 : u1 - u2 <=0 . What can you conclude?
| z value | (to 2 decimals) |
| p-value | (to 4 decimals) |
The difference (is/ isn't) statistically significant.
b. Can you conclude that the year 2 score for Rite Aid is above the national average 75.7 of ? Use ax .05 and null hypothesis is H0 u <= 75.7 . Enter negative value as negative number.
| zvalue | (to 2 decimals) |
| p-value | (to 4 decimals) |
We (can/ can not) conclude that customer service has improved for Rite Aid.
c. For Expedia, is the increase from year 1 to year 2 statistically significant? Use ax= .05 and null hypothesis is H0: u1-u2 <= 0.
| zvalue | (to 2 decimals) |
| p-value | (to 4 decimals) |
The difference (is/ isn't) statistically significant.
d. When conducting a hypothesis test with the values given for the standard deviation, sample size, and , how large must the increase from Year 1 to Year 2 be for it to be statistically significant?
(to 2 decimals)
e. Use the result of part (d) to state whether the increase for J.C. Penney from year 1 to year 2 is statistically significant.
The increase (is/ isn't) statistically significant.
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