5. Incorrect. The answer is false, not true

If the two classes come from two populations with means μ1 and μ 2. Then the test of hypothesis can be formulated as

H0: μ1= μ 2

H0: μ1≠ μ 2

Under H0 both classes come from the same population. The mean and the standard deviation of the difference in means is given by

μ(`X1-`X2)=0 and σ(`X1-`X2)=[(σ12/n1)+ (σ22/n2)]0.5=[82/50 + 72/60]0.5=1.4479

where we have used sample standard deviations as estimates of σ1 and σ2.

Then Z=(`X1-`X2)/σ(`X1-`X2)=(75-78)/1.4479=-2.07.

For a two-tailed test the results are significant at 5% level, since the results lie outside the range of -1.96 to 1.96. Hence we conclude that there is a significant difference in performance of the two classes at 5% level of significance.

For a two-tailed test the results are insignificant at 1% level, since the results lie within the range of -2.58 to 2.58. Hence we conclude that there is no significant difference in performance of the two classes at 1% level of significance.