2 Construct the 99 confidence interval for the difference Mu

2.

Construct the 99% confidence interval for the difference Mu 1 - Mu 2 when Round answers to two decimal places. A 99% confidence interval for the difference in the population means is

Solution

The degree of freedom =n1+n2-2= 21+25-2 = 44

Given a=1-0.99=0.01, t(0.005, df=44) =2.69 (from student t table)

So the lower bound is

(xbar1-xbar2) - t*sqrt(s1^2/n1+s2^2/n2)

=(477.21-322.45)-2.69*sqrt(39.59^2/21+29.5^2/25)

=126.62

So the upper bound is

(xbar1-xbar2) + t*sqrt(s1^2/n1+s2^2/n2)

=(477.21-322.45)+2.69*sqrt(39.59^2/21+29.5^2/25)

=182.90