**5. Correct. The answer is false**

If the two classes come from two
populations with means μ_{1} and μ_{ 2}. Then the
test of hypothesis can be formulated as

H_{0:} μ_{1}=
μ_{ 2}

H_{0:} μ_{1}≠
μ_{ 2}

Under H_{0} both classes
come from the same population. The mean and the standard deviation of the
difference in means is given by

μ(`X_{1}-`X_{2})=0 and σ(`X_{1}-`X_{2})=[(σ_{1}^{2}/n_{1})+ (σ_{2}^{2}/n_{2})]^{0.5}=[8^{2}/50 + 7^{2}/60]^{0.5}=1.4479

where we
have used sample standard deviations as estimates of σ_{1} and σ_{2}.

Then Z=(`X_{1}-`X_{2})/σ(`X_{1}-`X_{2})=(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.