Answer
There is sufficient evidence to reject that the weights have a standard deviation of 567.
Work Step by Step
$H_{0}:σ=567$. $H_{a}:σ < 567.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(81-1)^2 466^24}{567^2}=54.038.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.995}^2=51.172$, $X_{0.005}^2=116.321$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:51.172<54.038<116.321, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to reject that the weights have a standard deviation of 567.
