Answer
There is sufficient evidence to support that the standard deviation is more than 32.2.
Work Step by Step
$H_{0}:σ=32.2$. $H_{a}:σ >32.2.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(12-1)^2 52.441^2}{32.2^2}=29.176.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.05}^2=19.675.$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:19.676<29.176, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the standard deviation is more than 32.2.
