Answer
There is not sufficient evidence to reject that the speeds have a standard deviation equal to 5.
Work Step by Step
$H_{0}:σ=5$. $H_{a}:σ\ne5.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(12-1)^2 4.0751^2}{5^2}=7.307.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.95}^2=4.575, X_{0.05}^2=19.675$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:4.575<7.307<19.675, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to reject that the speeds have a standard deviation equal to 5.
