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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 0.012 Recent 77 91 89 78 57 101 62 87 69 87 81 84 57 82 73 103 60 Past 90 89 93 94 64 84 85 92 87 91 89 91 Let u, be the recent times and let ₂ be the past times. What are the null and alternative hypotheses? OA Ho: 4₁ = 1₂ H₁: P₁ P2 OC. Ho: H₁ H₂ H₁ H₁ H2 Calculate the test statistic. t=(Round to two decimal places as needed.) B. Ho: H1 H2 H₁:₁₂ OD. Ho: H1 H₂ H₁: H1 H2

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 0.012 Recent 77 91 89 78 57 101 62 87 69 87 81 84 57 82 73 103 60 Past 90 89 93 94 64 84 85 92 87 91 89 91 Let u, be the recent times and let ₂ be the past times. What are the null and alternative hypotheses? OA Ho: 4₁ = 1₂ H₁: P₁ P2 OC. Ho: H₁ H₂ H₁ H₁ H2 Calculate the test statistic. t=(Round to two decimal places as needed.) B. Ho: H1 H2 H₁:₁₂ OD. Ho: H1 H₂ H₁: H1 H2

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Find t and p value and construct a confidence interval

### Time Interval Data for Geyser Eruptions **Introduction:** The following dataset represents the time intervals (in minutes) between eruptions of a geyser. The data is categorized into "recent" times, which are within the past few years, and "past" times, which are from around 20 years ago. Both samples are assumed to be independent simple random samples from normally distributed populations. The objective is to determine if the mean time interval between eruptions has changed over time. **Data Table:** | | Eruption Intervals (min) | |----------------|--------------------------------| | **Recent** | 77, 91, 89, 78, 57, 101, 62, 87, 69, 87, 81, 84, 57, 82, 73, 103, 60 | | **Past** | 90, 89, 93, 94, 64, 84, 85, 92, 87, 91, 89, 91 | **Hypothesis Testing:** Let \(\mu_1\) be the mean recent time intervals and \(\mu_2\) be the mean past time intervals. **Question:** What 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 From the given image, **Option B** is selected. **Calculate the Test Statistic:** To determine if the mean time interval has changed, we need to calculate the test statistic \( t \). **Formula:** \[ t = \frac{(\bar{X}_1 - \bar{X}_2)}{\sqrt{\left(\frac{S_1^2}{n_1}\right) + \left(\frac{S_2^2}{n_2}\right)}}
Transcribed Image Text:### Time Interval Data for Geyser Eruptions **Introduction:** The following dataset represents the time intervals (in minutes) between eruptions of a geyser. The data is categorized into "recent" times, which are within the past few years, and "past" times, which are from around 20 years ago. Both samples are assumed to be independent simple random samples from normally distributed populations. The objective is to determine if the mean time interval between eruptions has changed over time. **Data Table:** | | Eruption Intervals (min) | |----------------|--------------------------------| | **Recent** | 77, 91, 89, 78, 57, 101, 62, 87, 69, 87, 81, 84, 57, 82, 73, 103, 60 | | **Past** | 90, 89, 93, 94, 64, 84, 85, 92, 87, 91, 89, 91 | **Hypothesis Testing:** Let \(\mu_1\) be the mean recent time intervals and \(\mu_2\) be the mean past time intervals. **Question:** What 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 From the given image, **Option B** is selected. **Calculate the Test Statistic:** To determine if the mean time interval has changed, we need to calculate the test statistic \( t \). **Formula:** \[ t = \frac{(\bar{X}_1 - \bar{X}_2)}{\sqrt{\left(\frac{S_1^2}{n_1}\right) + \left(\frac{S_2^2}{n_2}\right)}}
### Statistical Testing of Mean Body Temperature Differences Between Genders **The P-value is 0.071. (Round to three decimal places as needed.)** #### State the Conclusion for the Test: - **A. Reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.** - **B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.** **(Selected Answer)** - **C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.** - **D. Reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.** #### Conclusion Explanation: In this case, we fail to reject the null hypothesis because the P-value (0.071) is greater than the common significance level (α = 0.05). This indicates that there is not sufficient evidence to support the claim that men have a higher mean body temperature than women. #### Confidence Interval: - **b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.** The confidence interval is given as: \[ -0.28 < \mu_1 - \mu_2 < 1.16 \] **(Round to three decimal places as needed.)** #### Confidence Interval Explanation: The provided confidence interval suggests that the true difference in mean body temperatures between men and women (µ₁ - µ₂) can range from -0.28 to 1.16. Since this interval includes zero, it further supports the conclusion that there is not sufficient evidence to assert that men have a higher mean body temperature than women.
Transcribed Image Text:### Statistical Testing of Mean Body Temperature Differences Between Genders **The P-value is 0.071. (Round to three decimal places as needed.)** #### State the Conclusion for the Test: - **A. Reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.** - **B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.** **(Selected Answer)** - **C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.** - **D. Reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.** #### Conclusion Explanation: In this case, we fail to reject the null hypothesis because the P-value (0.071) is greater than the common significance level (α = 0.05). This indicates that there is not sufficient evidence to support the claim that men have a higher mean body temperature than women. #### Confidence Interval: - **b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.** The confidence interval is given as: \[ -0.28 < \mu_1 - \mu_2 < 1.16 \] **(Round to three decimal places as needed.)** #### Confidence Interval Explanation: The provided confidence interval suggests that the true difference in mean body temperatures between men and women (µ₁ - µ₂) can range from -0.28 to 1.16. Since this interval includes zero, it further supports the conclusion that there is not sufficient evidence to assert that men have a higher mean body temperature than women.
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