A study was conducted using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.10 significance level for both parts.---**Table:**| | Treatment (\(\mu_1\)) | Placebo (\(\mu_2\)) ||------------|--------------------|------------------|| \(n\) | 27 | 38 || \(\bar{x}\) | 2.36 | 2.63 || \(s\) | 0.56 | 0.94 |---**a.** Test the claim that the two samples are from populations with the same mean.What are the null and alternative hypotheses?- **A.** \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 < \mu_2 \)- **B.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \)- **C.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \)- **D.** \( H_0: \mu_1 < \mu_2 \) \( H_1: \mu_1 \geq \mu_2 \) ### Testing the Claim of Equal Population Means#### a. Hypothesis TestingTest the claim that the two samples are from populations with the same mean.**Null and Alternative Hypotheses**- **Option A:** \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 < \mu_2 \)- **Option B:** \( H_0: \mu_1 < \mu_2 \) \( H_1: \mu_1 \geq \mu_2 \)- **Option C:** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \)- **Option D:** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \)**Test Statistic and P-Value**- The test statistic, \( t \), is: \_\_\_ (Round to two decimal places as needed.)- The P-value is: \_\_\_ (Round to three decimal places as needed.)**Conclusion for the Test**- **A.** Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. - **B.** Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. - **C.** Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. - **D.** Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.#### b. Confidence Interval ConstructionConstruct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.\[ \mu_1 - \mu_2 = \_\_\_ \](Round to three decimal places as needed.)

Formula Used: Test-statistic t = X1-X2s12n1+s22n2 Confidence Interval = X1-X2 ± t*s12n1+s22n2

Answered: A study was done using a treatment…

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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A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Treatment Placebo μ μ1 μ2 n 27 39 x 2.38 2.65 s 0.87 0.61 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? 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 Your answer is correct. The test statistic, t, is (Round to two decimal places as needed.)

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