Question

Assume the university is interested in the question of whether the instructor impacts student learning. Professor A has a class of 28 students having an average grade of 84 and standard deviation of 6. Professor B has a class of 31 students having an average grade of 77 with a standard deviation of 8. Conduct a pooled-variance test using a 0.05 level of significance to determine whether Professor A is a better teacher than Professor B.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 > μ2

Pooled Variance
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((28 - 1)*6^2 + (31 - 1)*8^2)/(28 + 31 - 2))*(1/28 + 1/31))
sp = 1.8571

Test statistic,
t = (x1bar - x2bar)/sp
t = (84 - 77)/1.8571
t = 3.769

P-value Approach
P-value = 0.0002
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that professor A is a better teacher than Professor B