Female X123750 S12250 n120 Male X123800 S22300 n216SolutionL

Female: X₁=23,750; S₁²=250; n1=20

Male: X₁=23,800; S₂²=300; n2=16

Solution

Let mu1 be the mean for Female

Let mu2 be the mean for Male

Ho: mu1=mu2 (i.e. null hypothesis)

Ha: mu1<mu2 (i.e. alternative hypothesis)

The test statistic is

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

=(23750-23800)/sqrt(250/20+300/16)

=-8.94

It is a left-tailed test.

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

Given a=0.05, the critical value is t(0.05, df=34) = -1.69 (from student t table)

Since t=-8.94 is less than -1.69, we reject the null hypothesis.

So we can conclude that male nurses earn more than female nurses