Question

the national average for verbal section of the graduate record exam

Answer 1

Problem:

The national average for the verbal section of the Graduate Record Exam (GRE) is 500 with a standard deviation of 100. A researcher uses a sampling distribution made up of samples of 100.

According to the central limit theorem, what is the mean of the sampling distribution of means?

According to the central limit theorem, what is the standard error of the mean?

As you increase the number of subjects in your sample, the calculated value of a t test will…

a. Increase

b. Decrease

c. Remain the same

Keeping everything else the same, if you were to decrease your alpha level from .05 to .01, the likelihood of rejecting the null hypothesis…

a. Increases

b. Decreases

c. Remains the same

Solution:

Given:

Sample size, n =100

Mean, =500

Standard deviation, =100

Now,

According to the Central Limit Theorem, the mean of the sampling distribution of means is, =500

According to the Central Limit Theorem, the standard error of the mean is, =100/ =10

As you increase the number of subjects in your sample, the calculated value of a t test will increase.

(because, t =​​​​​​; so as n increases, t will increase and vice versa).
So option a. Increase is correct.

Keeping everything else the same, if you were to decrease your alpha level from .05 to .01, the likelihood of rejecting the null hypothesis decreases.

(because the rejection region decreases).
So, option b. Decreases is correct.