The per-store daily customer count (i.e., the mean number
of customers in a store in one day) for a nationwide convenience
store chain that operates nearly 10,000 stores has been
steady, at 900, for some time. To increase the customer count,
the chain is considering cutting prices for coffee beverages. The
question to be determined is how much to cut prices to increase
the daily customer count without reducing the gross margin on
ISBN 1-269-14496-0
Business Statistics: A First Course, Sixth Edition, by David M. Levine, Timothy C. Krehbiel, and Mark L. Berenson. Published by Prentice Hall.
Copyright © 2013 by Pearson Education, Inc.
Problems for Section 10.5 379
coffee sales too much. You decide to carry out an experiment in
a sample of 24 stores where customer counts have been running
almost exactly at the national average of 900. In 6 of the
stores, the price of a small coffee will now be $0.59, in 6 stores
the price of a small coffee will now be $0.69, in 6 stores, the
price of a small coffee will now be $0.79, and in 6 stores, the
price of a small coffee will now be $0.89. After four weeks of
selling the coffee at the new price, the daily customer count in
the stores was recorded and stored in .
a. At the 0.05 level of significance, is there evidence of a
difference in the daily customer count based on the price
of a small coffee?
b. If appropriate, determine which prices differ in daily customer
counts.
c. At the 0.05 level of significance, is there evidence of a
difference in the variation in daily customer count among
the different prices?
d. What effect does your result in (c) have on the validity of
the results in (a) and (b)?
10.62 Integrated circuits are manufactured on silicon wafers
through a process that involves a series of steps. An experiment
was carried out to study the effect on the yield of using three
methods in the cleansing step (coded to maintain confidentiality).
The results (stored in Yield-OneWay ) are as follows:
CoffeeSales
To answer these questions, you'll need to conduct hypothesis tests and analyze the data. Here are the steps you can follow to find the answers:
a. In order to determine whether there is evidence of a difference in the daily customer count based on the price of a small coffee, you need to perform an analysis of variance (ANOVA) test. It will help you compare the means of the different price groups.
1. Define hypotheses:
- Null hypothesis (H0): There is no difference in the daily customer count based on the price of a small coffee.
- Alternative hypothesis (Ha): There is a difference in the daily customer count based on the price of a small coffee.
2. Calculate the test statistic and p-value using ANOVA. This can be done using statistical software like R, Excel, or Python.
3. Determine the significance level (α) you want to test at. In this case, it is given as 0.05.
4. Compare the p-value with the significance level. If the p-value is less than the significance level, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
b. If you reject the null hypothesis in part a, you can perform post-hoc tests to determine which prices differ in daily customer counts. Common post-hoc tests include Tukey's HSD or pairwise t-tests with appropriate adjustments for multiple comparisons. These tests will help you identify the specific price groups that are significantly different from each other.
c. To determine if there is evidence of a difference in the variation in daily customer count among the different prices, you need to conduct a test for equality of variances, such as Levene's test or Bartlett's test. These tests will assess if there are significant differences in variability among the price groups.
d. The result in part c, if significant, suggests that the assumption of equal variances may not hold. This can affect the validity of the results in parts a and b because ANOVA assumes equal variances among groups. If there are unequal variances, it may impact the interpretation of any significant differences in means found in part a.
In summary, you will need to perform an ANOVA test to answer question a, followed by post-hoc tests to determine differences between specific price groups (question b). Additionally, you should conduct a test for equality of variances (question c) to assess the validity of the results from questions a and b.