91Ó°ÊÓ

The Normal requirement requires no outliers and that the distribution is approximately normally distributed.

Given is that the data set contains no outliers.

The sample size of $50$ is $30$ or more and thus we can assume that the distribution is approximately normal.

Thus the Normal requirement has been satisfied.

$n=50$

$\stackrel{¯}{x}=165.00$

$s=20.00$

Determine the hypotheses:

$H_0:\mathrm{μ}=\$158$

$H_0:\mathrm{μ}≠\$158$

Determine the value of the test statistic:

localid="1650365213749" $t=\frac{\stackrel{¯}{x}-{\mathrm{μ}}_0}{s/\sqrt{n}}$

$=2.475$

The $p$-value is the likelihood of getting the test statistic's value or a number that is more severe. The $p$-value is the number (or interval) in Table B's column header for the $t$-value in row localid="1650365294990" $n-1=50-1$

$=49>40$:

localid="1650365319262" $0.01=2×0.005<P<2×0.01$

$=0.02$

The null hypothesis is rejected if the$P$-value is less than the significance level.

$P<0.05=5\%⇒\text{Reject}{H}_0$