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 question states that the data is normally distributed, equal variances, and the sample sizes are greater than 30, we can use the two-sample t-test. Based on the data given, the point estimate for the difference in means is -7.62. Using a 95% confidence level, with a two-tailed test and 58 degrees of freedom, the t-value is 2.002. We can then calculate the margin of error by multiplying the standard error (2.258) by the t-value (2.002) which gives 4.52. To find the upper limit of the interval estimate, we add the margin of error to the point estimate which gives 6.20. Therefore, the statement is false and the upper limit of the interval estimate is not approximately $13.82.

The Cranston Hardware Company Is Interested in Estimating the Difference