Answer:
The critical values are 101.879 and 60.391.
Step-by-step explanation:
A hypothesis test for variance is performed to test whether the variance of all commute times is equal to 4.0 minutes.
The hypothesis for this test is:
H₀: The variance of all commute times is equal to 4.0 minutes, i.e.σ² = 4.
Hₐ: The variance of all commute times is equal to 4.0 minutes, i.e.σ² ≠ 4.
The test statistic is:
[tex]\chi^{2}=\frac{ns^{2}}{\sigma^{2}}[/tex]
Decision rule:
If the test statistic value is less than [tex]\chi^{2}_{(\alpha/2 ),(n-1)}[/tex] or greater than [tex]\chi^{2}_{(1-\alpha/2 ),(n-1)}[/tex] then the null hypothesis is rejected.
The significance level of the test is, α = 0.10.
The degrees of freedom is, n - 1 = 81 - 1 = 80
Compute the critical values as follows:
[tex]\chi^{2}_{(\alpha/2 ),(n-1)}=\chi^{2}_{(0.10/2 ),(81-1)}=\chi^{2}_{0.05, 80}=101.879[/tex]
[tex]\chi^{2}_{(1-\alpha/2 ),(n-1)}=\chi^{2}_{(1-0.10/2 ),(81-1)}=\chi^{2}_{(0.95),(80)}=60.391[/tex]
*Use a Chi-square table.
Thus, the critical values are 101.879 and 60.391.
