Question

A well-known buyer’s guide uses a 100-point customer satisfaction score to rate the nation’s major chain
stores. Assume that from past experience with the satisfaction score, a population variance of 144 is expected.
In 2019, Walmart was the only chain store to earn an outstanding rating for overall quality. However, critics
argue that although their average was higher, so to was the variance. A sample of 30 Walmart customer
satisfaction scores showed an average of 91.4 with a sample standard deviation of 14.3. You’ve been asked to
test the critics’ claim at a maximum allowable exposure to a Type I error of 10%.

Answer 1

As we are testing here whether the variance has increased from the population variance of 144, therefore this is a right tailed test here.

The test statistic here is computed as:

For n - 1 = 29 degrees of freedom, the p-value here is computed from the chi square distribution tables here as:

As the p-value here is 0.0664 < 0.1 which is the level of significance, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the spread has increased for walmart