Question 1074674
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.