An examination was given to two classes consisting of $40$ and $50$ students, respectively. In the first class, the mean grade was $74$ with a standard deviation of $8$, while in the second class the mean grade was $78$ with a standard deviation of $7$. Is there a significant difference between the performance of the two classes at a level of significance of $(a)$ $0.05$, $(b)$ $0.0$, $(c)$ What is the P value of the test?
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My question is why $8$ and $7$ have been taken as $σ$, not S if $78$ and $74$ are taken as $x̅$