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:
<em>H₀</em>: The population variance of all commute times is equal to 4.0 minutes, i.e. <em>σ² </em>= 4.
<em>Hₐ</em>: The population variance of all commute times is not equal to 4.0 minutes, i.e. <em>σ² </em>≠ 4.
The test statistic is:
The critical region of this test is defined as:
Reject <em>H₀</em> if or
.
The degrees of freedom is:
Compute the critical from a Chi-square table.
The test statistic value is, .
The null hypothesis is rejected because the test statistic is in the critical region.
Thus, the correct option is (a).