The objective is to check whether the mean test scores of the two groups significantly differ at the 0.05 level.
Let denote the mean of the participants participated in the survey after studying for one hour continuously.
Let denote the mean of the participants participated in the survey after studying for three twenty-minute sessions.
The null hypothesis is that there is no difference between the mean test of scores between the two groups. That is,
The alternative hypothesis is that there is a difference between the mean test of the score between the two groups. That is,
The level of significance is,
The formula for pooled variance is,
The test statistic is computed below.
The degrees of freedom is,
Computation of p value:
from the alternative hypothesis,it is clear that the test is a two- tailed test.
t represents the test statistic and df is the degrees of freedom p value
Reject the null hypothesis if p value is less than the level of significance.
That is, p value
Here the p value is 0.017503 is less than 0.05. So, reject the null hypothesis and conclude that there is a significant difference between the means of the two groups.