Question

Brainliest + 20 pts to whoever helps pls!!

Answer 1

Answer:

Correct option is (a). 60.391 and 101.879; because the test statistic is in a critical region, the test rejects the null hypothesis.

Step-by-step explanation:

A Chi-square test for population variance is used to perform this test.

The standard deviation is, 2.0 minutes.

Then the variance is, 4.0 minutes.

The hypothesis for this test is:

H₀: The population variance of all commute times is equal to 4.0 minutes, i.e. σ² = 4.

Hₐ: The population variance of all commute times is not equal to 4.0 minutes, i.e. σ² ≠ 4.

The test statistic is:

$\chi^{2}_{calc.}=\frac{(n-1)s^{2}}{\sigma^{2}}$

The critical region of this test is defined as:

Reject H₀ if $\chi^{2}_{calc.}$ or $\chi^{2}_{calc.}>\chi^{2}_{(1-\alpha /2), (n-1)}$.

The degrees of freedom is:

$n-1=81-1=80$

Compute the critical from a Chi-square table.

$\chi^{2}_{\alpha /2, (n-1)}=\chi^{2}_{0.05, 80}=101.879\\\chi^{2}_{(1-\alpha /2), (n-1)}=\chi^{2}_{0.95, 80}=60.391$

The test statistic value is, $\chi^{2}_{calc.}=105.8$.

$\chi^{2}_{calc.}=105.8 > \chi^{2}_{0.05, 80}=101.879$

The null hypothesis is rejected because the test statistic is in the critical region.

Thus, the correct option is (a).