91Ó°ÊÓ

$M=\$71,121,S=\$7489,n=41,a=0.05$

State the hypothesis:

The null hypothesis states that the average annual salary for registered California nurses is less than or equal to $\$69,110$. In symbols:

$H_0:\mathrm{μ}≤\$69,110$

The alternative hypothesis states that the average annual salary for registered California nurses is higher than $\$69,110$. In symbols:

$H_a:\mathrm{μ}>\$69,110$

The degree of freedom is:

$$\begin{gathered} df=n-1 \\ =41-1 \\ =40 \end{gathered}$$

From the t distribution table, for a right-tailed test with $a=0.05\text{for}df=40$, the critical value of t values or the critical region are $t=1.684$.

The test statistic is:

$$\begin{gathered} t=\frac{M-\mathrm{μ}}{S/\sqrt{n}} \\ =\frac{71,121-69,110}{7489\sqrt{41}} \\ =\frac{2011}{1169.585} \\ =1.72 \end{gathered}$$

We may infer that the average yearly income for registered California nurses is more than$\$69,110$ since the null hypothesis was rejected.