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Lake Martin and Lake Fields are two large local lakes inhabited by white sturgeon. A while back there was an environmental disaster at Lake Martin. Kala is an ecologist who wants to see if the mean weight (in kg) of adult white sturgeon now living in Lake Martin is less than the mean weight (in kg) of adult white sturgeon now living in Lake Fields. The ecologist catches a random sample of 11 adult white sturgeon at Lake Martin and a random sample of 12 adult white sturgeon at Lake Fields. (These samples are chosen independently.) Each fish has its weight (in kg) recorded. The white sturgeon caught at Lake Martin have a sample mean weight of 90.24 with a sample variance of 15.11. The white sturgeon caught at Lake Fields have a sample mean weight of 98.52 with a sample variance of 231.20. Assume that the two populations of weights are approximately normally distributed. Can the ecologist conclude, at the 0.01 level of significance, that the population mean of the weights of adult white sturgeon now living in Lake Martin is less than the population mean of the weights of adult white sturgeon now living in Lake Fields? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternate hypothesis H₁. H:0 H₁:0 (b) Determine the type of test statistic to use. (Choose one) V (c) Find the value of the test statistic. (Round to three or more decimal places.) Explanation Check μ XI 9 0=0 ☐☐ a S OSO 0<0 Р O Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Acces

Lake Martin and Lake Fields are two large local lakes inhabited by white sturgeon. A while back there was an environmental disaster at Lake Martin. Kala is an ecologist who wants to see if the mean weight (in kg) of adult white sturgeon now living in Lake Martin is less than the mean weight (in kg) of adult white sturgeon now living in Lake Fields. The ecologist catches a random sample of 11 adult white sturgeon at Lake Martin and a random sample of 12 adult white sturgeon at Lake Fields. (These samples are chosen independently.) Each fish has its weight (in kg) recorded. The white sturgeon caught at Lake Martin have a sample mean weight of 90.24 with a sample variance of 15.11. The white sturgeon caught at Lake Fields have a sample mean weight of 98.52 with a sample variance of 231.20. Assume that the two populations of weights are approximately normally distributed. Can the ecologist conclude, at the 0.01 level of significance, that the population mean of the weights of adult white sturgeon now living in Lake Martin is less than the population mean of the weights of adult white sturgeon now living in Lake Fields? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternate hypothesis H₁. H:0 H₁:0 (b) Determine the type of test statistic to use. (Choose one) V (c) Find the value of the test statistic. (Round to three or more decimal places.) Explanation Check μ XI 9 0=0 ☐☐ a S OSO 0<0 Р O Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Acces

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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### Educational Example: Statistical Comparison of White Sturgeon Weights **Context:** Lake Martin and Lake Fields are two large local lakes inhabited by white sturgeon. Kala, an ecologist, is interested in determining if the mean weight of adult white sturgeon now living in Lake Martin is less than those in Lake Fields after an environmental disaster affected Lake Martin. **Data Collection:** - Sample from Lake Martin: 11 adult white sturgeon - Sample from Lake Fields: 12 adult white sturgeon - Measurements: - Lake Martin: - Sample Mean Weight = 90.24 kg - Sample Variance = 15.11 - Lake Fields: - Sample Mean Weight = 98.52 kg - Sample Variance = 231.20 **Assumptions:** - Weights are approximately normally distributed. - Population means are compared at a 0.01 level of significance. **Objective:** Can the ecologist conclude that the mean weight of adult white sturgeon in Lake Martin is less than in Lake Fields? **Statistical Analysis Steps:** 1. **Hypothesis Formulation:** - Null Hypothesis \( H_0 \): Mean weight in Lake Martin \( \geq \) Mean weight in Lake Fields - Alternative Hypothesis \( H_1 \): Mean weight in Lake Martin \( < \) Mean weight in Lake Fields 2. **Determine the Type of Test Statistic:** - Choose an appropriate test (e.g., t-test for means) depending on sample sizes and variance equality. 3. **Calculate the Test Statistic:** - Round off intermediate computations to three or more decimal places to maintain precision. 4. **Decision Making:** - Compare the calculated statistic value with critical values or p-values at 0.01 significance level to make a statistical decision whether to reject \( H_0 \) or not. **Visual Aids:** - Boxes or symbols next to \( \mu, \sigma, \rho, \overline{X}, S, \hat{p} \) to represent data and statistical elements. - Diagrams indicating relationships between hypothesis symbols and statistical values for test selection and computation guidance. **Conclusion:** Carry out these statistical steps and check results using the platform tools for explanation and verification.
Transcribed Image Text:### Educational Example: Statistical Comparison of White Sturgeon Weights **Context:** Lake Martin and Lake Fields are two large local lakes inhabited by white sturgeon. Kala, an ecologist, is interested in determining if the mean weight of adult white sturgeon now living in Lake Martin is less than those in Lake Fields after an environmental disaster affected Lake Martin. **Data Collection:** - Sample from Lake Martin: 11 adult white sturgeon - Sample from Lake Fields: 12 adult white sturgeon - Measurements: - Lake Martin: - Sample Mean Weight = 90.24 kg - Sample Variance = 15.11 - Lake Fields: - Sample Mean Weight = 98.52 kg - Sample Variance = 231.20 **Assumptions:** - Weights are approximately normally distributed. - Population means are compared at a 0.01 level of significance. **Objective:** Can the ecologist conclude that the mean weight of adult white sturgeon in Lake Martin is less than in Lake Fields? **Statistical Analysis Steps:** 1. **Hypothesis Formulation:** - Null Hypothesis \( H_0 \): Mean weight in Lake Martin \( \geq \) Mean weight in Lake Fields - Alternative Hypothesis \( H_1 \): Mean weight in Lake Martin \( < \) Mean weight in Lake Fields 2. **Determine the Type of Test Statistic:** - Choose an appropriate test (e.g., t-test for means) depending on sample sizes and variance equality. 3. **Calculate the Test Statistic:** - Round off intermediate computations to three or more decimal places to maintain precision. 4. **Decision Making:** - Compare the calculated statistic value with critical values or p-values at 0.01 significance level to make a statistical decision whether to reject \( H_0 \) or not. **Visual Aids:** - Boxes or symbols next to \( \mu, \sigma, \rho, \overline{X}, S, \hat{p} \) to represent data and statistical elements. - Diagrams indicating relationships between hypothesis symbols and statistical values for test selection and computation guidance. **Conclusion:** Carry out these statistical steps and check results using the platform tools for explanation and verification.
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(d) Find the p-value. (Round to three or more decimal places.) (e) At the 0.01 level of significance, can the ecologist conclude that the mean weight of adult white sturgeon now living in Lake Martin is less than the mean weight of adult white sturgeon now living in Lake Fields? OYes O No Explanation Check X 2022 McGraw Hill LLC. All Rights Res
Transcribed Image Text:(d) Find the p-value. (Round to three or more decimal places.) (e) At the 0.01 level of significance, can the ecologist conclude that the mean weight of adult white sturgeon now living in Lake Martin is less than the mean weight of adult white sturgeon now living in Lake Fields? OYes O No Explanation Check X 2022 McGraw Hill LLC. All Rights Res
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