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What is your conclusion about the following hypotheses of the difference in population means using following information and significance level a = .20? Suppose The samples are selected independent the populations are normally distributed. - Hoi Hn - H2 = 0 Hai H₁-H₂ #0 Sample 1 n1=31 = 51.9 X1 0²₁ = 49 O a. Reject the null hypothesis O b. Fail to reject the null hypothesis O c. There is not enough information O d. None of them Sample 2 n2 = 32 X₂ = 53.5 0²2 = 64

What is your conclusion about the following hypotheses of the difference in population means using following information and significance level a = .20? Suppose The samples are selected independent the populations are normally distributed. - Hoi Hn - H2 = 0 Hai H₁-H₂ #0 Sample 1 n1=31 = 51.9 X1 0²₁ = 49 O a. Reject the null hypothesis O b. Fail to reject the null hypothesis O c. There is not enough information O d. None of them Sample 2 n2 = 32 X₂ = 53.5 0²2 = 64

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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### Question 4 #### Hypothesis Testing for Difference in Population Means Given the following information and a significance level \(\alpha = 0.20\), suppose the samples are selected independently and the populations are normally distributed. The hypotheses to test are: Null Hypothesis (\(H_0\)): \(\mu_1 - \mu_2 = 0\) Alternative Hypothesis (\(H_a\)): \(\mu_1 - \mu_2 \neq 0\) ##### Sample Data - **Sample 1**: - Sample size (\(n_1\)) = 31 - Sample mean (\(\overline{x}_1\)) = 51.9 - Sample variance (\(\sigma_1^2\)) = 49 - **Sample 2**: - Sample size (\(n_2\)) = 32 - Sample mean (\(\overline{x}_2\)) = 53.5 - Sample variance (\(\sigma_2^2\)) = 64 ##### Conclusion Options: a. Reject the null hypothesis b. Fail to reject the null hypothesis c. There is not enough information d. None of them To determine the correct conclusion, one would typically calculate the test statistic (often using a t-test for independent means if population variances are unknown but assumed to be approximately equal or unequal based on sample data). Using the given significance level, we would then compare the test statistic to the critical value or use a p-value approach to make a decision regarding the null hypothesis.
Transcribed Image Text:### Question 4 #### Hypothesis Testing for Difference in Population Means Given the following information and a significance level \(\alpha = 0.20\), suppose the samples are selected independently and the populations are normally distributed. The hypotheses to test are: Null Hypothesis (\(H_0\)): \(\mu_1 - \mu_2 = 0\) Alternative Hypothesis (\(H_a\)): \(\mu_1 - \mu_2 \neq 0\) ##### Sample Data - **Sample 1**: - Sample size (\(n_1\)) = 31 - Sample mean (\(\overline{x}_1\)) = 51.9 - Sample variance (\(\sigma_1^2\)) = 49 - **Sample 2**: - Sample size (\(n_2\)) = 32 - Sample mean (\(\overline{x}_2\)) = 53.5 - Sample variance (\(\sigma_2^2\)) = 64 ##### Conclusion Options: a. Reject the null hypothesis b. Fail to reject the null hypothesis c. There is not enough information d. None of them To determine the correct conclusion, one would typically calculate the test statistic (often using a t-test for independent means if population variances are unknown but assumed to be approximately equal or unequal based on sample data). Using the given significance level, we would then compare the test statistic to the critical value or use a p-value approach to make a decision regarding the null hypothesis.
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