Question

A clinical trial was designed to compare a new drug for lowering cholesterol to a placebo. The 100 subjects who took the new drug had a mean cholesterol of 180.5 with a standard deviation of 23.3. The 100 subjects who took the placebo had a mean cholesterol of 204.1 with a standard deviation of 22.1. Construct a two-sided 95% confidence interval for the difference between the two means, assuming equal variance. Give an interpretation of the confidence interval. You MUST show your work to receive full credit. Partial credit is available.

Answer 1

Confidence interval is :-
( X̅1 - X̅2 ) ± t( α/2 , n1+n2-2) SP √( (1/n1) + (1/n2))
Critical value t(α/2, n1 + n1 - 2) = t( 0.05/2, 100 + 100 - 2) = 1.972 ( from t table )

( 180.5 - 204.1 ) ± t(0.05/2 , 100 + 100 -2) 22.7079 √ ( (1/100) + (1/100))
Lower Limit = ( 180.5 - 204.1 ) - t(0.05/2 , 100 + 100 -2) 22.7079 √( (1/100) + (1/100))
Lower Limit = -29.9328
Upper Limit = ( 180.5 - 204.1 ) + t(0.05/2 , 100 + 100 -2) 22.7079 √( (1/100) + (1/100))
Upper Limit = -17.2672
95% Confidence Interval is ( -29.9328 , -17.2672 )

We are 95% confidence that the true population mean difference lies within the interval ( -29.9328 , -17.2672 ).

Since the interval contain only negative values, we can conclude that new drug lowered the cholesterol level.