Answer
We fail to reject the null hypothesis (there is not enough evidence to conclude that $\sigma \ne 5.2$).
Work Step by Step
Here we have $H_{o}$:σ = 5.2, $H_{1}: σ \ne 5.2$, n = 18, s = 4.9, df = n-1 = 17
α = 0.05, α/2 = 0.025, 1 - α/2 = 0.975
$χ2_{α/2} = 30.191$, $χ2_{1-α/2} = 7.564$
We have: 30.191 < 15.095 < 7.564
Hence, we fail to reject the null hypothesis (there is not enough evidence to conclude that $\sigma \ne 5.2$).
