5. Correct. The answer is false

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

H_0: μ₁= μ ₂

H_0: 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(`X<sub>1</sub>-`X₂)=0 and σ(`X<sub>1</sub>-`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=(`X<sub>1</sub>-`X₂)/σ(`X<sub>1</sub>-`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.