1 **Geyser Eruption Interval Analysis****Data Overview:**Listed below are time intervals (in minutes) between eruptions of a geyser. The "recent" times are within the past few years, while the "past" times are from around 20 years ago. The two samples are independent simple random samples from normally distributed populations. The assumption is made that the population standard deviations are equal.Recent Eruption Intervals (min): - 78, 91, 88, 79, 57, 101, 63, 76, 87, 73, 103, 60Past Eruption Intervals (min): - 70, 98, 93, 94, 65, 86, 86, 91, 91, 94, 71, 80**Hypothesis Testing:**Define:- μ₁: Mean of the recent times- μ₂: Mean of the past timesWhat are the null and alternative hypotheses?Options:- A. - H₀: μ₁ ≠ μ₂ - H₁: μ₁ = μ₂- B. - H₀: μ₁ = μ₂ - H₁: μ₁ ≠ μ₂- C. - H₀: μ₁ = μ₂ - H₁: μ₁ > μ₂- D. - H₀: μ₁ < μ₂ - H₁: μ₁ = μ₂**Test Statistic Calculation:**Calculate the test statistic t:t = _____ (Round to two decimal places as needed.)**P-Value:**Find the P-value:P-value = _____ (Round to three decimal places as needed.)**Conclusion:**Make a conclusion about the null hypothesis and address the original claim using a significance level of 0.10.Evaluate: H₀ because the P-value is _____ the significance level. There _____ sufficient evidence that the mean time interval has changed.**Options:**- A. Yes, the conclusion is affected by the significance level because H₀ is rejected when the significance level is 0.10 but is not rejected when it is 0.01.- B. No, the conclusion is not affected by the significance level because H₀ is rejected

Answered: Image /qna-images/answer/21f2268a-e86c-4a75-8484-ea9df2738787.jpg

Listed below are time intervals (min) between eruptions of a geyser. Assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Does it appear that the mean time interval has changed? Is the conclusion affected by whether the significance level is 0.10 or 0.01? Recent 78 91 88 79 57 101 63 87 70 88 83 83 56 81 73 103 60 D Past 90 88 93 94 65 86 86 92 86 91 91 91 Let u, be the recent times and let uz be the past times. What are the null and alternative hypotheses? O A. Hoi H H2 O B. Ho: H = P2 H: H #2 OC. H H=H2 OD. Ho: H