hypothesis testing

Question

an examination was given to two classes each consisting of 49 students. In the first class the mean marks were 74 with a standard deviation of 8; in the second class the mean marks were 78 with a standard deviation of 9. Is it reasonable to regard the two classes as having been obtained from the same normal population? Test your hypothesis at 1% level of significance.

Answer 1

Ho: mu1 = mu2

Ha: mu1 != mu2

n1 = 49 xbar1 = 74 SD1 = 8

n2 = 49 xbar2 = 78 SD2 = 9

t = (xbar1 - xbar2)/sqrt(SD1^2/n1 + SD2^2/n2) = (74 - 78)/sqrt(64/49 + 81/49) = -2.33

p-value = P(t < -2.33)*2 at 7 DOF = 0.0263 *2 = 0.0526

since p-value > 0.01, then fail to reject Ho and it is reasonable to regard the two classes as having been obtained from the same normal population.