Independent Sample T-Test

Question

"A Statistics teacher wants to compare her two classes to see if they performed any differently on the test she gave that semester. Class A had 25 students with an average score of 70, standard deviation 15. Class B had 20 students with an average score of 74, standard deviation 25. Using alpha 0.05, did these two classes performed differently on the tests?" Please answer ASAP, I still don't have the idea on how to compute these kinds of questions and im new in Statistics Subject.. Thank you!

Answer 1

This requires the t-test for two independent samples (2 classes) and unequal variance (since the standard deviation for each class is different)

Calculate the t value from the data, compare the critical value, and then determine whether there is sufficient information in the data to agree that they are the same (null hypothesis) or not agree ( reject the null hypothesis).

Null Hypothesis (status quo) the two groups performed similarly, that is, H0 : Mean 1 = Mean 2.

Alternative Hypothesis (demonstrate difference ) that is, H1: Mean1 ≠ Mean 2

t = {mean1 - mean2} / {sqrt( var1/n1 + var2/n2) }

= {70 - 74} / {sqrt (225/25 + 625/20)}

= -4 / {sqrt (9 + 31.25)}

= -.6304

Crirical value from t - table, for .05 level of significance, 43 degrees of freedom (n1 + n2 -2), is approx 2.017

So we need t values less than -2.017 to be significant at the .05 level of significance. Since -.6304 is not smalled than -2.017, we see that there is not enough evidence from the sample to support the conclusion that the two classes performed differently on the exam.