Question

Independent random samples are selected from two populations. The summary statistics are given below. Assume unequal variances for the questions below. m = 5 x ̅ = 12.7 s1 = 3.2

n = 7 y ̅ = 9.9 s2 = 2.1

a) Construct a 95% confidence interval for the difference of the means.

b) Using alpha = 0.05, test if the means of the two populations are different based on the result from part (a). Explain your answer.

Answer 1

Ans:

a)

As,unequal variances assumed,so df=5-1=4 (as we consider smaller of m-1 or n-1 as df)

critical t value=tinv(0.05,4)=2.776

Margin of error=2.776*sqrt((3.2^2/5)+(2.1^2/7))=4.54

Point estimate for difference=12.7-9.9=2.8

95% confidence interval for difference in means

=2.8+/-4.54

=(-1.74, 7.34)

b)

As,the above confidence interval includes 0 within its limits,there is not sufficient evidence to conclude that the means of the two populations are different.