A random sample of n25 individuals is selected from a popula

A random sample of n=25 individuals is selected from a population with u=20, and a treatment is administered to each individual in the sample. After treatment the sample mean is found to be m=22.2 with SS=384. How much difference is there between the mean for the treated sample and the mean for the original population?

based on two tail P 0.05

what would be the t value?

ciritical t value?

standard error?

I did the beginning part of the problem.

Solution

mean1 eq: 20 (variance= 384.16) (se= 3.92)
mean2 eq: 22.5 (variance= 384.16) (se= 3.92)

Probability that var1<var2
p=0.5 (left: 0.5; double: 1)

Difference between means:
M1-M2=20-22.5=-2.5
sd=38.408; se=5.5437
95% CI of difference:
-13.3655 <-2.5< 8.3655 (Wald)
t-difference: -0.451
df-t: 47.5; p= 0.32702
(left p: 0.673; two sided: 0.654)
Difference not significant at 5%