The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers.It wishes to estimate this difference using a 95 percent confidence level.Assume that the variances are equal and the populations normally distributed.The following data represent independent samples from each population:
Based on these data,the upper limit of the interval estimate is approximately $13.82.

Question

The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers.It wishes to estimate this difference using a 95 percent confidence level.Assume that the variances are equal and the populations normally distributed.The following data represent independent samples from each population:
  Based on these data,the upper limit of the interval estimate is approximately $13.82.

Quizplus · Accepted Answer

Since the problem states that the confidence level is 95%, we are using a two-tailed t-test. From the given data, we can calculate the sample means, the pooled standard deviation, and the standard error of the difference in means. Using the t-distribution with (n1 + n2 - 2) degrees of freedom, we can find the critical value for a 95% confidence level. We can then use the standard error and the critical value to find the margin of error, which is added and subtracted from the difference in sample means to get the confidence interval. The upper limit of this interval is $13.82, which means that there is a 95% chance that the true difference in means lies somewhere below this value. Therefore, the answer is A, true.

The Cranston Hardware Company Is Interested in Estimating the Difference