Answer
There is not sufficient evidence to reject that the Oscar winning actresses' mean age is 33 years.
Work Step by Step
$H_{0}:\mu=33$. $H_{a}:\mu \ne33.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{35.9-33}{11.1/\sqrt{82}}=2.37.$ The P-value is the probability of z being less than -2.37 or bigger than 2.37 which is the sum of the probability of the z-score being less than -2.37 plus 1 minus the probability of the z-score being less than 2.37, hence:P=0.0089+1-0.9911=0.0178. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is more than $\alpha=0.01$, because it is 0.0178, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to reject that the Oscar winning actresses' mean age is 33 years.
