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 t 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 interval has changed? Is the conclusion affected by whether the significance level is 0.10 or 0.01? Recent 77 91 90 78 56 101 62 87 69 88 82 84 56 80 74 103 61 89 87 93 94 63 86 86 92 87 91 88 91 Past Let u, be the recent times and let ₂ be the past times. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁ H₁ H₂ OC. Ho: H₁ = H₂ H₁ H₁ H₂ Calculate the test statistic. t= (Round to two decimal places as needed.). Find the P-value. OB. Ho: H1 H2 H₁: H₁ H₂ OD. Ho: H₁ H₁ H₁ H₂ H₂

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**Time Interval Analysis of Geyser Eruptions**

**Introduction**

Listed below are time intervals (minutes) between eruptions of a geyser. Assume that the "recent" times are within the past few years, and the "past" times are from around 20 years ago. 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 interval has changed? Consider the conclusion affected by whether the significance level is 0.10 or 0.01.

**Data:**

- **Recent Times:** 77, 91, 90, 78, 56, 101, 62, 87, 69, 88, 82, 84, 56, 80, 74, 103, 61
- **Past Times:** 89, 87, 93, 94, 63, 86, 92, 87, 91, 88, 91

**Step-by-Step Instructions:**

1. **Formulate Hypotheses:**

   Let \( \mu_1 \) be the recent times and \( \mu_2 \) be the past times.

   **Which of the following are the null and alternative hypotheses?**

   - A. \( H_0: \mu_1 \ne \mu_2 \)  \( H_1: \mu_1 = \mu_2 \)
   - B. \( H_0: \mu_1 = \mu_2 \)  \( H_1: \mu_1 > \mu_2 \)
   - C. \( H_0: \mu_1 = \mu_2 \)  \( H_1: \mu_1 \ne \mu_2 \)
   - D. \( H_0: \mu_1 < \mu_2 \)  \( H_1: \mu_1 = \mu_2 \)
   
2. **Calculate the Test Statistic:**

   - Compute the value of \( t \) (Round to two decimal places as needed).
   
3. **Find the P-Value:**

   - Determine the P-value (Round to three decimal places as needed).

4. **Make a Conclusion:**

   - Based on the P-value, make a conclusion about the null hypothesis. Use a
Transcribed Image Text:**Time Interval Analysis of Geyser Eruptions** **Introduction** Listed below are time intervals (minutes) between eruptions of a geyser. Assume that the "recent" times are within the past few years, and the "past" times are from around 20 years ago. 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 interval has changed? Consider the conclusion affected by whether the significance level is 0.10 or 0.01. **Data:** - **Recent Times:** 77, 91, 90, 78, 56, 101, 62, 87, 69, 88, 82, 84, 56, 80, 74, 103, 61 - **Past Times:** 89, 87, 93, 94, 63, 86, 92, 87, 91, 88, 91 **Step-by-Step Instructions:** 1. **Formulate Hypotheses:** Let \( \mu_1 \) be the recent times and \( \mu_2 \) be the past times. **Which of the following are the null and alternative hypotheses?** - A. \( H_0: \mu_1 \ne \mu_2 \) \( H_1: \mu_1 = \mu_2 \) - B. \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \) - C. \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \ne \mu_2 \) - D. \( H_0: \mu_1 < \mu_2 \) \( H_1: \mu_1 = \mu_2 \) 2. **Calculate the Test Statistic:** - Compute the value of \( t \) (Round to two decimal places as needed). 3. **Find the P-Value:** - Determine the P-value (Round to three decimal places as needed). 4. **Make a Conclusion:** - Based on the P-value, make a conclusion about the null hypothesis. Use a
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