46. Happy customers As the Hispanic population in the United States has grown, businesses have tried to understand what Hispanics like. One study inter-viewed a random sample of 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. Here are summary results for the importance of “reliability” (the accuracy of account records and so on):

(a) The distribution of reliability ratings in each group is not Normal. A graph of the data reveals no outliers. The use of two-sample t procedures is
justified. Why?
(b) Construct and interpret a $95\%$ confidence interval for the difference between the mean ratings of the importance of reliability for Anglo and
Hispanic bank customers.
(c) Interpret the $95\%$ confidence level in the context of this study.

The summary results for the importance of “reliability” is:

Let, assume the sample sizes are $92$and $86$, which are both greater than the required sample size of $30$, implying that the distribution is normally distributed..

Therefore, the distribution is about normal because the sample sizes$(92/86)$ are at least $30$.
At least $30$ in sample size is required.

A $95\%$confidence interval for the difference between the mean ratings of the importance of reliability for Anglo and Hispanic bank customers.

Using a $Ti-83$ calculator, the $95\%$confidence interval for the difference between the mean wages of female and male university students can be determined as follows:

The confidence interval thus becomes$(0.2264,0.6936)$

Therefore, the mean difference in ratings has a $95\%$of probability is between $0.2264$and $0.6936$.

To interpret the $95\%$confidence level in the context of this study.

Since, the $95\%$confidence interval means that $95\%$ of all available samples will have a confidence interval that includes the genuine population mean difference between the mean ratings of the significance of reliability for Anglo and Hispanic bank customers.