A researcher suggests that male nurses earn more than female

A researcher suggests that male nurses earn more than female nurses. A survey of 16 male nurses and 20 female nurses reported the following data. Create a 90% confidence interval for the difference between Male and Female salaries

Female: X₁=23,750; S₁²=250; n1=20

Male: X₁=23,800; S₂²=300; n2=16

Solution

The degree of freedom =n1+n2-2=16+20-2 = 34

Given a=0.1, t(0.05, df=34) = 1.69 (from student t table)

So 90% confidence interval is

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

-->(23750-23800) +/- 1.69*sqrt(250/20+300/16)

--> (-59.44739, -40.55261)