Question

Suppose we are testing the hypotheses H0 : μ = 100 and Ha: μ < 100. Which sample mean will have the smaller p-value, x = 90 or x = 85? Select all that apply. x = 85 will have a smaller p-value because it is further from μ0 = 100. x = 90 will have a smaller p-value because it is closer to μ0 = 100. x = 85 will have a smaller p-value because it provides more support for HA. x = 90 will have a smaller p-value because it provides more support for HA.

Answer 1

Option C: x = 85 will have a smaller p-value because it provides more support for HA

Explanation:

Looking at all the options, the only one that is correct is option C because from the area under the normal distribution curve, the left tail of x-bar = 85 has a smaller value then the left-tail of x-bar = 90 and thus it supports the hypothesis Ha: μ < 100. The other options don't support either of the hypothesis. Thus,

We can say then that x = 85 will have a smaller p-value because it provides more support for HA