Problem
Statistics Zoe Kerr $11 / 20 / 2310: 19$ PM a Claim about a Question 14, Instructor-created HW Score: $63.33 \%, 9.5$ of 15 points question Points: 0 of 1 Save A teacher claims that her students' test scores are getting more consistent and now have a lower variation than 2.31 , the variation in previous terms. She conducts a hypothesis test. She calculates her test statistic to be $\chi^{2}=17.945$ She looks up the critical value for this test and finds it to be $\chi^{2}=20.721$. What can she conclude? Hint: Set-up $\mathrm{Ho}$ and $\mathrm{H}_{1}$ first, draw a sketch and read the answer choices carefully! A. The test statistic falls in the critical (rejection) region for this test. Therefore, there is sufficient evidence to support her claim. B. The test statistic does not fall in the critical (rejection) region for this test. Therefore, there is sufficient evidence to support her claim. C. The test statistic falls in the critical (rejection) region for this test. Therefore, there is not sufficient evidence to support her claim. D. The test statistic does not fall in the critical (rejection) region for this test. Therefore, there is not sufficient evidence to support her claim.
Solution
Step 1 ：Define the null hypothesis (H0) as the variation is not lower than 2.31.
Step 2 ：Define the alternative hypothesis (H1) as the variation is lower than 2.31.
Step 3 ：Compare the test statistic (17.945) with the critical value (20.721).
Step 4 ：Since the test statistic is less than the critical value, we do not reject the null hypothesis.
Step 5 ：Therefore, there is not sufficient evidence to support the teacher's claim that the variation is lower than 2.31.
Step 6 ：\(\boxed{\text{The correct answer is D. The test statistic does not fall in the critical (rejection) region for this test. Therefore, there is not sufficient evidence to support her claim.}}\)
