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Use the information provided to answer the questions. Population Sample Size Sample Mean Sample Variance USE SALT 1 2 17 12 34.9 32.3 4.4 5.4 State the null and alternative hypotheses for testing for a significant difference in means. O Ho: (M₁M₂) = 0 versus H₂: (M₁₂) <0 O Ho: (M₁M₂) = 0 versus H₂: (μ₁ −μ₂) * 0 O Ho: (M₁M₂) = 0 versus H₂: (₁₂) > 0 O Ho: (M₁M₂) #0 versus H₂: (μ₁ − ₂) = 0 O Ho: (M₁M₂) < 0 versus H₂: (H₁-H₂) >0 t< Calculate the pooled estimate of o2, the associated degrees of freedom, and the observed value of the t statistic. (Round s² and your t statistic to three decimal places.) s² = df = t = What is the rejection region using a = 0.05? (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

Use the information provided to answer the questions. Population Sample Size Sample Mean Sample Variance USE SALT 1 2 17 12 34.9 32.3 4.4 5.4 State the null and alternative hypotheses for testing for a significant difference in means. O Ho: (M₁M₂) = 0 versus H₂: (M₁₂) <0 O Ho: (M₁M₂) = 0 versus H₂: (μ₁ −μ₂) * 0 O Ho: (M₁M₂) = 0 versus H₂: (₁₂) > 0 O Ho: (M₁M₂) #0 versus H₂: (μ₁ − ₂) = 0 O Ho: (M₁M₂) < 0 versus H₂: (H₁-H₂) >0 t< Calculate the pooled estimate of o2, the associated degrees of freedom, and the observed value of the t statistic. (Round s² and your t statistic to three decimal places.) s² = df = t = What is the rejection region using a = 0.05? (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

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
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**Statistical Analysis: Understanding p-values and Hypothesis Testing** **What can be said about the p-value for the test?** - ○ p-value < 0.010 - ○ 0.010 < p-value < 0.020 - ○ 0.020 < p-value < 0.050 - ○ 0.050 < p-value < 0.100 - ○ 0.100 < p-value < 0.200 - ○ p-value > 0.200 **What can you conclude from these data?** - ○ \( H_0 \) is not rejected. There is insufficient evidence to conclude that there is a significant difference between the population means. - ○ \( H_0 \) is not rejected. There is sufficient evidence to conclude that there is a significant difference between the population means. - ○ \( H_0 \) is rejected. There is sufficient evidence to conclude that there is a significant difference between the population means. - ○ \( H_0 \) is rejected. There is insufficient evidence to conclude that there is a significant difference between the population means.
Transcribed Image Text:**Statistical Analysis: Understanding p-values and Hypothesis Testing** **What can be said about the p-value for the test?** - ○ p-value < 0.010 - ○ 0.010 < p-value < 0.020 - ○ 0.020 < p-value < 0.050 - ○ 0.050 < p-value < 0.100 - ○ 0.100 < p-value < 0.200 - ○ p-value > 0.200 **What can you conclude from these data?** - ○ \( H_0 \) is not rejected. There is insufficient evidence to conclude that there is a significant difference between the population means. - ○ \( H_0 \) is not rejected. There is sufficient evidence to conclude that there is a significant difference between the population means. - ○ \( H_0 \) is rejected. There is sufficient evidence to conclude that there is a significant difference between the population means. - ○ \( H_0 \) is rejected. There is insufficient evidence to conclude that there is a significant difference between the population means.
### Statistical Analysis for Difference in Means #### Data Summary **Population Details:** | | Population 1 | Population 2 | |---------------|--------------|--------------| | Sample Size | 17 | 12 | | Sample Mean | 34.9 | 32.3 | | Sample Variance | 4.4 | 5.4 | #### Hypotheses Testing Choose the appropriate null and alternative hypotheses for testing a significant difference in means: - \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) < 0 \) - \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) \neq 0 \) - \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) > 0 \) - \( H_0: (\mu_1 - \mu_2) \neq 0 \) versus \( H_a: (\mu_1 - \mu_2) = 0 \) - \( H_0: (\mu_1 - \mu_2) < 0 \) versus \( H_a: (\mu_1 - \mu_2) > 0 \) #### Calculation Requirements Calculate the following, rounding to three decimal places: - **Pooled Estimate of \(\sigma^2\):** \( s^2 = \) - **Degrees of Freedom (df):** \( df = \) - **Observed Value of the t-statistic:** \( t = \) #### Rejection Region Determine the rejection region using \(\alpha = 0.05\). If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places: - \( t > \) - \( t < \) This activity involves analyzing sample data to test specific hypotheses related to population means, utilizing statistical tools for accurate assessment of data characteristics and inference.
Transcribed Image Text:### Statistical Analysis for Difference in Means #### Data Summary **Population Details:** | | Population 1 | Population 2 | |---------------|--------------|--------------| | Sample Size | 17 | 12 | | Sample Mean | 34.9 | 32.3 | | Sample Variance | 4.4 | 5.4 | #### Hypotheses Testing Choose the appropriate null and alternative hypotheses for testing a significant difference in means: - \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) < 0 \) - \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) \neq 0 \) - \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) > 0 \) - \( H_0: (\mu_1 - \mu_2) \neq 0 \) versus \( H_a: (\mu_1 - \mu_2) = 0 \) - \( H_0: (\mu_1 - \mu_2) < 0 \) versus \( H_a: (\mu_1 - \mu_2) > 0 \) #### Calculation Requirements Calculate the following, rounding to three decimal places: - **Pooled Estimate of \(\sigma^2\):** \( s^2 = \) - **Degrees of Freedom (df):** \( df = \) - **Observed Value of the t-statistic:** \( t = \) #### Rejection Region Determine the rejection region using \(\alpha = 0.05\). If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places: - \( t > \) - \( t < \) This activity involves analyzing sample data to test specific hypotheses related to population means, utilizing statistical tools for accurate assessment of data characteristics and inference.
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