Answer
There is not sufficient evidence to reject that the pulse rates have a standard deviation equal to 10.
Work Step by Step
$H_{0}:σ=10$. $H_{a}:σ\ne10.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(40-1)^2 11.6^2}{10^2}=52.478.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.975}^2=24.433, X_{0.025}^2=59.342.$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:24.433<52.478<59.342, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to reject that the pulse rates have a standard deviation equal to 10.
