Question

4. In the June 2007 issue, Consumer Reports examined the relative merits of top-loading and front-loading washing machines, testing samples of several different brands of each type. Suppose the study tested the null hypothesis that top-and front-loading machines don’t differ in their mean costs, and the test had a P-value of 0.32. Would a 95% confidence interval contain 0? Explain.

Please show all work. Typed work only. no handwritten.

Answer 1

SOLUTION:

From given data,

In the June 2007 issue, Consumer Reports examined the relative merits of top-loading and front-loading washing machines, testing samples of several different brands of each type. Suppose the study tested the null hypothesis that top-and front-loading machines don’t differ in their mean costs, and the test had a P-value of 0.32. Would a 95% confidence interval contain 0

A consumer report examined the relative menu atop loading and front loading machines

A test of null hypothesis that, there is no difference in mean costs of top loading machines and front loading machines, yields p value of 0.32 Here, the 95% confidence interval is constructed for - .

Here the difference in mean co. of top loading machines ( ) and mean cost of top loading machines ( ) is designated by - .

In this case comparing the p-value with the significance level 0.05, it is seen that the p-value is more than the significance level 0.05.

So the null hypothesis cannot be rejected.

This implies the 95% confidence interval tor the difference in mean cost of top loading machines and mean cost atop loading machines contains 0.

Since containing 0 in the confidence interval is the indication that the null hypothesis cannot be rejected

Thus, it can be concluded that, there is no sufficient evidence to state that there is a difference between difference in mean cost of top loading machines and mean cost of top loading machines