Elementary Statistics (12th Edition)

$H_{0}:σ=0.023$. $H_{a}:σ \ne0.023.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(35-1)^2 0.0493^2}{0.023^2}=156.213.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.01}^2=\frac{150.892+63.691}{2}=107.2915.$$X_{1-0.01}^2=\frac{14.954+22.164}{2}=18.559.$ If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:107.2915<156.213, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to support that the pennies have a standard deviation of 0.023.