Question

Researchers study the relationship between interpersonal violence and health in college age women. The selected an alpha of 0.05. The researchers wanted to see if there was a significant difference in the type of primary residence (home vs. student housing) for abused versus non abused college aged women. They report a p value of 0.35. You know this means:

Select There is an inadequate sample size. as your answer
There is an inadequate sample size.
Select A type II error has occurred. as your answer
A type II error has occurred.
Select There is a statistically significant difference in the type of primary residence for abused vs. non-abused college aged women. as your answer
There is a statistically significant difference in the type of primary residence for abused vs. non-abused college aged women.
Select There is not a statistically significant difference in the type of primary residence for abused vs. non-abused college aged women. as your answer
There is not a statistically significant difference in the type of primary residence for abused vs. non-abused college aged women.

Answer 1

Explained below.

Explanation:

A statistical hypothesis test is being performed to determine whether there was a significant difference in the type of primary residence (home vs. student housing) for abused versus non abused college aged women.

The hypothesis can be defined as:

H₀: There is no difference in the type of primary residence or abused versus non abused college aged women.

Hₐ: There is a significant difference in the type of primary residence or abused versus non abused college aged women.

The significance level of the test is:

α = 0.05

The computed p-value is:

p-value = 0.35

p-value = 0.35 > α = 0.05

The null hypothesis will not be rejected.

The p-value is inversely related to the sample size of the test.

That is, larger the sample size smaller is the p-value and smaller the sample size larger is the p-value.

A p-value of 0.35 is very large and unusual. This can happen because of the inadequate sample size selected.

As the p-value indicates an unusual result, it can be said that an error has been made while concluding that the null hypothesis is true, when in fact it is not.

This type of error is known as the type II error.

The correct decision should be:

There is a statistically significant difference in the type of primary residence for abused vs. non-abused college aged women.