Question

After a sample of n=25 high school students took a special training course, their SAT scores averaged Md= 18 points higher with SS= 9600. On the basis of this sample, can you conclude that the training course has a significant effect on SAT scores? Use a two-tailed test at the .05 level of significance.

Answer 1

Solution:
Given:

Sample Size = n = 25

Sample Mean of differences = Md= 18 points  higher

SS= 9600

level of significance = 0.05

We have to use two tailed test to test if the training course has a significant effect on SAT scores.

Thus we use following steps:

Step 1) State H0 and H1:

Vs

( Two tailed test)

Step 2) Find test statistic value:

where

thus

Step 3) Find t critical values:

df = n - 1 = 25 - 1 = 24

level of significance = two tail area = 0.05

t critical values = +/- 2.064

Step 4) Decision Rule:

Reject null hypothesis H0, if absolute t test statistic value > t critical value = 2.064, otherwise we fail to reject H0.

Since t test statistic value = 4.500 > t critical value = 2.064, we reject null hypothesis H0 at the 0.05 level of significance.

Step 5) Conclusion:

Since we have rejected H0, there is sufficient evidence to conclude that:  the training course has a significant effect on SAT scores