A data set lists earthquake depths. The summary statistics are \( n = 400 \), \( \bar{x} = 5.92 \, \text{km} \), \( s = 4.67 \, \text{km} \). Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 5.00. Assume that a simple random sample has been selected.**Determine the test statistic.**\(type your answer...)\*(Round to two decimal places as needed.)***Determine the P-value.**\(type your answer...)\*(Round to three decimal places as needed.)***State the final conclusion that addresses the original claim.**\(choose your answer...) \( H_0 \).There is (choose your answer...) evidence to conclude that the mean of the population of earthquake depths is 5.00 km (choose your answer...) correct. **Hypothesis Testing with a Drug Study**Suppose 249 subjects are treated with a drug that is used to treat pain, and 55 of them developed nausea. Use a 0.10 significance level to test the claim that more than 20% of users develop nausea.**Questions:**1. **The test statistic for this hypothesis test is:** *(Round to two decimal places as needed.)* *[Text box for answer input]*2. **The P-value for this hypothesis test is:** *(Round to three decimal places as needed.)* *[Text box for answer input]*3. **Identify the conclusion for this hypothesis test:** *[Dropdown menu for answer selection]*This task involves identifying the appropriate statistical measures and arriving at a conclusion based on the hypothesis test result.

Note: Hi there! Thank you for posting the question. As there are several independent questions, according to our policy we have solved the first question. If you need help with other question, please re post separately.Suppose μ is the population mean of earthquake depths. It is needed to test the claim that whether these earthquakes are from a population with a mean equal to 5. The null and alternative hypotheses are, Null hypothesis: H0: μ = 5. Alternative hypothesis: H1: μ ≠ 5. The test is two tailed. The sample size is n = 400. The sample is a simple random sample. Moreover, the sample size large (> 30) and the population standard deviation is not given. Hence, one sample t test is used. The sample mean is, x̅ = 5.92 and the sample standard deviation is s = 4.67. The test statistic is, t = (x̅ – μ) / (s/√n). = (5.92 – 5) / (4.67/√400) = 0.92/0.2335 ≈ 3.94 The test statistic is 3.94. The degrees of freedom is, df = n – 1 = 400 – 1 = 399. Now, using the EXCEL formula =T.DIST.2T(3.94,399) the P-value is obtained as approximately 0.000. The excel output is, Decision rule: If P-value is less than or equal to the level of significance, reject the null hypothesis. Otherwise fail to reject the null hypothesis. The level of significance is α = 0.01. Conclusion: The P-value of 0.000 is less than α = 0.01. Reject H0. There is enough evidence to conclude that the mean of the population of earthquake depths is 5.00 km is not correct.