Question

A researcher uses two samples, each with n = 15 participants, to evaluate the mean difference in performance scores between 8-year-old and 10-year-old children. The prediction is that the older children will have higher scores. The sample mean for the older children is five points higher than the mean for the younger children and the pooled variance for the two samples is 30. For a one- tailed test, what decision should be made? a. Reject the null hypothesis with a = .05 but not with a = .01. b. Reject the null hypothesis with either a = .05 or a = .01. c. Fail to reject the null hypothesis with a = .05 but not with a = 01. d. Fail to reject the null hypothesis with either a = .05 or c = .01.
please explain how to do this because i dont get it thank you

Answer 1

Ans:

Right tailed test.

(as claim is that older children will have higher scores)

pooled variance=30

standard error for difference=sqrt(30*((1/15)+(1/15)))=2

test statistic:

t=5/2

t=2.5

df=15+15-2=28

p-value=tdist(2.5,28,1)=0.0093

As,p-value is less than 0.05 and 0.01,we can reject the null hypothesis at both alpha=0.05 or 0.01

Option b is correct.

Reject the null hypothesis with either alpha=0.05 or alpha=0.01