Questions: State the null hypothesis, H₀, and the alternative hypothesis, Hₐ, that would be used

Transcript text: State the null hypothesis, $H_{0}$, and the alternative hypothesis, $H_{a}$, that would be used

Solution

Solution Steps

Step 1: Finding the critical chi-squared values

Given $\alpha = 0.05$ and $n=7$, the degrees of freedom are $df = n-1 = 7-1 = 6$. We are looking for the critical chi-squared values for a two-tailed test. $\chi^2_{1-\alpha/2, df} = \chi^2_{1-0.05/2, 6} = \chi^2_{0.975, 6} = 1.24$ $\chi^2_{\alpha/2, df} = \chi^2_{0.05/2, 6} = \chi^2_{0.025, 6} = 14.4$ When $\alpha=0.1$, $\chi^2_{0.95,6} = 1.64$ and $\chi^2_{0.05,6}=12.59$ When $\alpha=0$, $\chi^2_{1,6}$ and $\chi^2_{0,6}$ are undefined.

Step 2: Filling in the blanks

Based on the chi-squared distribution table, we have: $\chi^2(6, 0.05) = 12.59 \approx 12.6$ which is not equal to $32.671$ or $1.24$ or $14.4$ $\chi^2(6, 0.1)=10.64$ $\chi^2(6, 0) = 0$

$P(\chi^2>1.24)=0.975$ $P(\chi^2>14.4)=0.025$