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. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? A. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H2 H₁ H₁ H₂ The test statistic, t, is -1.45. (Round to two decimal places as needed.) The P-value is 0.153. (Round to three decimal places as needed.) State the conclusion for the test. C OB. Ho: H₁
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 X for both parts. Treatment Placebo H1 H2 In 31 40 2.35 2.66 0.67 0.95 ... C. Ho: H1 = H2 H1: Hy> H2 'D. Ho:H1 =H2 H,: H1 # H2 The test statistic, t, is - 1.61 . (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.)
Given in the table are the BMI statistics for random samples of men and women. 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 0.01 significance level for both parts. a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? OA. Ho: H=H H₁: Hy > H₂ ỌC. Ho: H=H2 H₁: H₁ H₂ 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. -C OB. Ho: ₁2/₂ H₁ H₁ H₂ OD. Ho. Hy#t H₁: H₁ H₂ O A. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. O B. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women…
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 0.10 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. Ho H1 H2 H₁: H1 H2 o C. Ho: H = 2 H₁: H1 H2 OB. Ho: H1 H2 H1 H1 H2 OD. Ho H1 H2 H₁: 12 Treatment Placebo μ H1 H2 n 27 31 X 2.35 2.65 S 0.95 0.55
Consider two populations in the same state. Both populations are the same size (22,000). Population 1 consists of all students at the State university. Population 2 consists of all residents in a small town. Consider the variable Age. Which population would most likely have the largest standard deviation? They would likely have the same standard deviation(SD) for age because they have the same population size. O Population 2 would more likely have a higher standard deviation (SD) than Population 1. Population 1 would more likely have a higher standard deviation(SD) than Population 2 There is not enough information to tell.
Treatment Placebo 3. H1 H2 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. A study was done using a treatment group and a placebo group. The results are shown in the 27 40 In 2.39 2.65 0.95 0.57 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? O A. Ho: H1 = H2 O B. Ho: H1H2 D. Ho: H1 H2 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. O A. 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. O B. Reject the null hypothesis. There is not sufficient evidence to warrant rejection…
Given in the table are the BMI statistics for random samples of men and women. 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 0.01 significance level for both parts. a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H₂ H₁ H₁ H₂ The test statistic, t, is The P-value is (Round to two decimal places as needed.) (Round to three decimal places as needed.) State the conclusion for the test. C O B. Ho: H=H2 H₁: H₁ H₂ OD. Ho Hy#t H₁: H₁ H₂ O A. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. O B. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the…
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Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. 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 0.01 significance level for both parts. a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: Hy #4₂ OC, Hoi ky tuy H₁: Hy O L P H command n X S Time Remaining: 01:13:11 V : • Diet H₁ 30 0.79861 lb 0.00445 lb ; x { [ option ? I Regular H₂ 30 0.80936 lb 0.00742 lb Next delete

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