Answer
There is sufficient evidence to support ages have a standard deviation less than 22.5.
Work Step by Step
$H_{0}:σ=22.5$. $H_{a}:σ<22.5.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(15-1)^2 7.67^2}{22.5^2}=1.629.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{1-0.01}^2=4.66$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:1.629<4.66, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support ages have a standard deviation less than 22.5.
