Question

A self-scan machine was recently installed at Giant Eagle. The store manager would like to know if the mean checkout time using the standard checkout method is longer than using the self-scan. She gathered the following information. She found from a sample of 39 standard checkout customers, their mean wait time was 5 minutes with a standard deviation of .5 minutes. For a sample of 46 self-scan customers their mean wait time was 4.6 minutes with a standard deviation of .56 minutes. Using a 5% significance level can we conclude the standard checkout has a longer wait? Please show all work hand written.

Answer 1

The test hypothesis is

This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side

Now, the value of test static can be found out by following formula:

Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 39 + 46 - 2 = 83

This implies that

Since , we reject the null hypothesis H0 in favor of the alternative hypothesis H1 at

Yes we can conclude the standard checkout has a longer wait