Question

Basic statistics course is offered in Harvard and Penn State both. In a test, the average score of 50 Harvard students is 75 points and standard deviation is 10 points where as for 45 Penn State students, these parameters are 72 points and 8 points respectively. Construct 94% confidence interval for the difference in the mean scores.

Answer 1

Confidence interval is :-
( X̅1 - X̅2 ) ± t( α/2 , n1+n2-2) SP √( (1/n1) + (1/n2))

t(α/2, n1 + n1 - 2) = t( 0.06/2, 50 + 45 - 2) = 1.904
( 75 - 72 ) ± t(0.06/2 , 50 + 45 -2) 9.1087 √ ( (1/50) + (1/45))
Lower Limit = ( 75 - 72 ) - t(0.06/2 , 50 + 45 -2) 9.1087 √( (1/50) + (1/45))
Lower Limit = -0.5636
Upper Limit = ( 75 - 72 ) + t(0.06/2 , 50 + 45 -2) 9.1087 √( (1/50) + (1/45))
Upper Limit = 6.5636
94% Confidence Interval is ( -0.5636 , 6.5636 )