From the question, we know the population standard deviation, σ = 1.63, the sample standard deviation, s = 3.07, the sample mean, [tex]\bar{x}=7.43[/tex] and the sample size, n = 38.
The question illustrates a hypothesis chi-square test of variance.
The test statistics for a Chi-squared test of variance is given by
[tex]T=(n-1)\left( \frac{s}{\sigma} \right)^2 \\ \\ =(38-1)\left( \frac{3.07}{1.63} \right)^2 \\ \\ =37(1.883)^2=37(3.5473) \\ \\ =131.25[/tex]
