A Supermarket Has Just Added a New Cash Register to Reduce

question 105

Essay

A supermarket has just added a new cash register to reduce the waiting times of the customers during weekends. Because a new cash register has been added, the customers expect their waiting time to be less than the waiting time had been before the cash register was added. Suppose the sample variance of the waiting times for 25 customers before adding the new cash register is = 4.8 minutes, while the sample variance of the waiting times for 25 customers after adding the cash register is = 2.2 minutes. The manager of the supermarket believes that the waiting times are normally distributed and that the two samples are drawn independently.
A) Develop the hypotheses to test whether the ratio of two population variances is less than 1.
B) Calculate the appropriate test statistic.
C) Using the p-value approach, what is the decision at the 5% significance level?
D) What is the conclusion? Given that all other criteria are satisfied, should the supermarket continue with the new cash register?

• A) Develop the hypotheses to test whether the ratio of two population variances is less than 1.
• B) Calculate the appropriate test statistic.
• C) Using the p-value approach, what is the decision at the 5% significance level?
• D) What is the conclusion? Given that all other criteria are satisfied, should the supermarket continue with the new cash register?

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Definitions:

Null Hypothesis

A hypothesis that there is no significant difference or effect, serving as the default assumption to be tested in statistical hypothesis testing.

One-Tailed Test

A statistical test in which the region of rejection is on only one side of the sampling distribution, used when making a directional hypothesis about a population parameter.

Hypothesize

The process of making an educated guess or proposition that attempts to explain a phenomenon or answer a question, which can then be tested through experimentation or observation.