Answer
There is not sufficient evidence to reject that the cigarettes have a standard deviation not equal to 3.2.
Work Step by Step
$H_{0}:σ=3.2$. $H_{a}:σ\ne3.2.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(25-1)^2 3.7^2}{3.2^2}=32.086.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.975}^2=12.401, X_{0.025}^2=39.364.$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:12.401<32.086<39.364, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to reject that the cigarettes have a standard deviation not equal to 3.2.
