## Elementary Statistics (12th Edition)

$H_{0}:σ=28.866$. $H_{a}:σ\ne28.866.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(100-1)^2 33.5^2}{28.866^2}=133.337.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.995}^2=67.328, X_{0.005}^2=140.169.$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:67.328<133.337<140.169, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to reject that the sample has a standard deviation of 28.866.