Question

A school boasts of its tutoring program offered to students.  Two samples of 71 students each are taken.  The first sample consists of students who have not taken part in the tutoring program while the second sample consists of students who have taken part in the tutoring program.  An aptitude test was given to both samples.  The first sample showed a mean score of 150 with a standard deviation of 20 while the second sample showed a mean score of 158 with a standard deviation of 23.  Using a significance level of 1%, can you conclude that the two samples are different?

Null Hypothesis: ____________________            Your Work:

Alternative Hypothesis: ____________________

Critical Value: ____________________

Test Statistic: ____________________

Your Decision: ____________________

Answer 1

As we are testing here whether the two means are equal, therefore the null and the alternative hypothesis here are given as:

The standard error is first computed here as:

Now for n1 + n2 - 2 = 140 degrees of freedom and 0.01 level of significance, we get from the t distribution tables here:

P( t140 < 2.611) = 0.995

Therefore, due to symmetry:
P( -2.611 < t140 < 2.611) = 0.99

Therefore -2.611, 2.611 are the required critical value here.

Now the test statistic is computed here as:

Therefore -2.2116 is the required critical value here.

As the test statistic value here lies in between the two critical values, therefore they are in non rejection region and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the two means are not equal.