Chapter 10: Q. 53. (page 668)

Happy customers As the Hispanic population in the United States has grown, businesses have tried to understand what Hispanics like. One study interviewed separate random samples of Hispanic and Anglo customers leaving a bank. Customers were classified as Hispanic if they preferred to be interviewed in Spanish or as Anglo if they preferred English. Each customer rated the importance of several aspects of bank service on a 10- point scale.25 Here are summary results for the importance of “reliability” (the accuracy of account records, etc.):
Researchers want to know if there is a difference in the mean reliability ratings of all Anglo and Hispanic bank customers.
a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.
b. Check that the conditions for performing the test are met.

Short Answer

Expert verified

Part a) The hypothesis is:

$H_{0} : μ_{1} = μ_{2} H_{a} : μ_{1} n o t e q u a l t o μ_{2}$

Part b) All conditions are met.

Step by step solution

Part a) Step 1: Given information

The given claim that a difference in the means.

Part a) Step 2: Explanation

We must now determine the appropriate hypotheses for performing a significance test.

As a result, the claim represents either the null hypothesis or the alternative hypothesis. According to the null hypothesis, the population proportions are equal. If the claim is the null hypothesis, then the alternative hypothesis states the inverse of the null hypothesis.

Therefore, the following are the appropriate hypotheses:

$H_{0} : μ_{1} = μ_{2} H_{a} : μ_{1} n o t e q u a l t o μ_{2}$

Where we have,

The true mean reliability rating of all Angle bank customers is $μ_{1}$

$μ_{2} =$ represents the true mean reliability rating of all Hispanic bank customers.

Part b) Step 1: Explanation

There are three requirements that must be met:

It is satisfying because the samples are drawn at random from different populations.

Independent: It is satisfying because the sample of $92$ Anglo customers is less than $10 %$ of the total Anglo customer population, and the sample of 86 Hispanic customers is less than $10 %$ of the total Hispanic customer population.

Normal: It is satisfying because both samples are large, with sample sizes of at least $30 .$

As a result, all of the conditions are met, and a hypothesis test for the mean difference is appropriate.