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. Use a 0.01 significance level for both parts.**Table Data:**| | Treatment | Placebo ||------------|-----------|---------|| n | 34 | 31 || x̄ | 2.39 | 2.64 || s | 0.59 | 0.93 |### a. Test the claim that the two samples are from populations with the same mean.**What are the null and alternative hypotheses?**- A. \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \)- B. \( H_0: \mu_1 < \mu_2 \) \( H_1: \mu_1 \geq \mu_2 \)- C. \( H_0: \mu_1 > \mu_2 \) \( H_1: \mu_1 \leq \mu_2 \)- D. \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \)### 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.)**State the conclusion for the test:**- A. 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.- B. 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.- C. 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.- 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. Construct

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Description: 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 popul

Given: Level of significance, α=0.01 Treatment Placebo μ μ1 μ2 n 34 31 x 2.39 2.64 s 0.59 0.93 (a) The null and alternative hypothesis are: Null Hypothesis, H0 :μ1 =μ2 Alternative Hypothesis, H1 : μ1 ≠μ2The test-statistic is given by: t=x1-x2s12n1+s12n1 Therefore, t=2.39-2.64(0.59)234+(0.93)231=-0.250.03813=-1.2803 So, t-statistics is -1.2803Since, this is a two tailed test, so the p-value is as follows: p-value=2×P tn1+n2-2>1.28=2×P t34+31-2>1.28=2×P (t63>1.28)=0.205238 Since, p-value is greater than significance level 0.01, so there are no sufficient evidence to reject the null hypothesis. Option (a) Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from population with the same mean.(b) Confidence interval: The formula is as follows: x1-x2±tdf, α2 s12n1+s22n2 Therefore, =(2.39-2.64)±t(63, 0.005)(0.59)234+(0.93)231=(2.39-2.64)±(2.6561)(0.59)234+(0.93)231=-0.25±0.5187=-0.7687, 0.2687 -0.769≤μ1-μ2≤0.269 So, the confidence interval contains the value 0, so we do not have sufficient evidence to reject the null hypothesis. So, yes the confidence interval support the conclusion found with the hypothesis test.

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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 parts (a) and (b) below. Use a 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Hg P"P2 OB. Ho

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 parts (a) and (b) below. Use a 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Hg P"P2 OB. Ho

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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