If the hypothesis $\sigma=0.20$ is tested against the hypothesis that $\sigma \neq 0.20$, with $\alpha=0.05$, based on a random sample of size $n=18$, then the appropriate tabled value(s) is(are)
A) $X_{0.05}^{2}$ only.
B) $X_{0.025}^{2}$ and $X_{0.975}^{2}$.
C) $X_{0.10}^{2}$ only.
D) $X_{0.025}^{2}$ only.

Question

Quizplus · Accepted Answer

This is a two-tailed test because the alternative hypothesis is $\sigma \neq 0.20$, so we look up the chi-square values at $\alpha/2 = 0.025$ and $1-\alpha/2 = 0.975$ to find the critical values for both tails of the distribution.

If the Hypothesis σ=0.20\sigma=0.20σ=0.20 Is Tested Against the Hypothesis That σ≠0.20\sigma \neq 0.20σ=0.20

If the Hypothesis $\sigma=0.20$ Is Tested Against the Hypothesis That $\sigma \neq 0.20$