An organisation developing a new drug to combat depression i

An organisation developing a new drug to combat depression is perfroming testing on ten subjects.After giving 10mg of the drug to each subject for 30 days,psychological tests are given to evaluate the drugs performance.The results of the test are on a scale of 100 given in the table.If the mean and variance of the psychological test prior to taaking the drug was 61 and 89,respectively,comment on the performance of the drug using the two-sample t test with alpha=0.01.

Solution

alpha,a = 0.01
n1 = 10 , xbar1 = 61 , s1 = sqrt(89) = 9.434
n2 = 10 , xbar2 = 72.4 , s2 = 13.566

H0: u1 = u2
H1: u1 < u2

standard error, SE = sqrt((s1^2/n1)+(s2^2/n2))
SE = sqrt((9.434^2/10) + (13.566^2/10)) = 5.22529

test statistic, t = (xbar1-xbar2) / SE
t = (61-72.4) / 5.22529 = -2.182

critical value = -t(a,n1+n2-2) = - t(0.01, 18)
critical value = -2.552
since t > critical value, hence H0 can not be rejected
so we can not conclude that new drug is effective for depression