SOLUTION: " The performance of 50 teachers in the Science Department showed a mean of 98 with a standard deviation of 9.2. A sample of 40 teachers from the English Department showed an avera

Question 1074674: " The performance of 50 teachers in the Science Department showed a mean of 98 with a standard deviation of 9.2. A sample of 40 teachers from the English Department showed an average performance of 95 with a standard deviation of 7.3. If the level of significance is 1%, would you agree to the claim that the Science Department has higher performance than the English Deartment?"
thank you.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is a two sample t-test, and assuming normality and that sd of the random samples are reasonable approximations of the true sd
the test stat
is a t=(x1 bar-x2 bar)/(sqrt ((s1^2/n1)+s2^2/n2)) and the critical value for 88 df is about t>1.66, because this is a one way test, given that the question asks whether one is larger than the other, not whether there is a difference.
numerator is 3
denominator is sqrt(1.69+1.33)=sqrt(3.02)=1.74
The test-statistic value is 3/1.74=1.72 and we reject Ho and accept the claim that the Science Department has a higher performance with a p-value of 0.044.
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