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 the questions in the given problem, we need to perform a statistical analysis on the data provided. Let's break down the steps and calculations for each part:

a. To determine if there is evidence of a difference in the daily customer count based on the price of a small coffee, we will perform a one-way analysis of variance (ANOVA) test.

1. Calculate the mean daily customer count for each price level (0.59, 0.69, 0.79, 0.89) using the data provided.

2. Calculate the overall mean daily customer count across all price levels.

3. Calculate the sum of squares between groups (SSB), which represents the variation between the means of each price level. This can be calculated by multiplying the number of observations in each price level by the squared difference between the price level mean and the overall mean, and summing these values for all price levels.

4. Calculate the sum of squares within groups (SSW), which represents the variation within each price level. This can be calculated by summing the squared differences between each individual daily customer count and its respective price level mean, for all price levels.

5. Calculate the F-statistic by dividing the SSB by the SSW and dividing it by the degrees of freedom between groups (number of price levels - 1). The degrees of freedom within groups is the total number of observations minus the number of price levels.

6. Compare the calculated F-statistic to the critical F-value at the 0.05 level of significance with the appropriate degrees of freedom. If the calculated F-statistic is greater than the critical F-value, there is evidence of a difference in the daily customer count based on the price of a small coffee.

b. If there is evidence of a difference in daily customer counts, we can determine which prices differ by performing post hoc tests, such as Tukey's Honestly Significant Difference (HSD) test or pairwise t-tests. These tests compare the means of different price levels and identify significant differences between them.

c. To determine if there is evidence of a difference in the variation in daily customer count among the different prices, we can perform a test for homogeneity of variances, such as Levene's test. This test compares the variances of the daily customer counts across different price levels.

d. The result in (c) would indicate whether the assumption of equal variances is valid for the ANOVA test in (a). If there is evidence of a significant difference in variation among the different prices, it may affect the validity of the results in (a) and the interpretation of the post hoc tests in (b). In such cases, alternative tests or adjustments may need to be considered.

Note: The calculations and specific tests mentioned here are general procedures commonly used in statistical analysis. The actual implementation may involve software or statistical packages for ease and accuracy.