Student advisors are interested in determining if the variances of the scores of day students and night students are the same. The following samples are drawn. Day (population 1): n1 = 25, s1 = 9.8; Night (population 2): n2 = 31, s2 = 14.7. Let and o2 be the respective population standard deviation. We want to test the null hypothesis that of = o, with 0.05 as significant level. Use Sf/s5 as your test statistic. Please answer the following questions using decimal. Do NOT use, for example, "10.2%" as your answer. Instead, type 0.102 as your answer. The observed value of the test statistic is 2.25 . (round to the nearest ten thousandth) The p-value of this hypothesis test is 0.977 (round to the nearest thousandth) The smaller critical value of the test statistic is 0.468 . (round to the nearest thousandth) The larger critical value of the test statistic is 2.209 (round to the nearest thousandth)

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ANswer Question 4 with all four parts including an explaination. Please ignore my claculations and the answers that I have posted in the blanks. 

**Question 4**

Student advisors are interested in determining if the variances of the scores of day students and night students are the same. The following samples are drawn. Day (population 1): \( n_1 = 25, \, s_1 = 9.8 \); Night (population 2): \( n_2 = 31, \, s_2 = 14.7 \). Let \(\sigma_1\) and \(\sigma_2\) be the respective population standard deviation.

We want to test the null hypothesis that \(\sigma_1^2 = \sigma_2^2\) with 0.05 as significant level. Use \(\frac{s_1^2}{s_2^2}\) as your test statistic. Please answer the following questions using decimal. Do NOT use, for example, "10.2%" as your answer. Instead, type 0.102 as your answer.

- The observed value of the test statistic is \(\boxed{2.25}\) (round to the nearest ten thousandth)
- The p-value of this hypothesis test is \(\boxed{0.977}\) (round to the nearest thousandth)
- The smaller critical value of the test statistic is \(\boxed{0.468}\) (round to the nearest thousandth)
- The larger critical value of the test statistic is \(\boxed{2.209}\) (round to the nearest thousandth)
Transcribed Image Text:**Question 4** Student advisors are interested in determining if the variances of the scores of day students and night students are the same. The following samples are drawn. Day (population 1): \( n_1 = 25, \, s_1 = 9.8 \); Night (population 2): \( n_2 = 31, \, s_2 = 14.7 \). Let \(\sigma_1\) and \(\sigma_2\) be the respective population standard deviation. We want to test the null hypothesis that \(\sigma_1^2 = \sigma_2^2\) with 0.05 as significant level. Use \(\frac{s_1^2}{s_2^2}\) as your test statistic. Please answer the following questions using decimal. Do NOT use, for example, "10.2%" as your answer. Instead, type 0.102 as your answer. - The observed value of the test statistic is \(\boxed{2.25}\) (round to the nearest ten thousandth) - The p-value of this hypothesis test is \(\boxed{0.977}\) (round to the nearest thousandth) - The smaller critical value of the test statistic is \(\boxed{0.468}\) (round to the nearest thousandth) - The larger critical value of the test statistic is \(\boxed{2.209}\) (round to the nearest thousandth)
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