Treatment Placebo lu 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 n (b) below. Use a 0.05 significance level for both parts. 27 2.31 0.86 H2 39 2.67 0.56 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? O B. Ho: P H2 O A. Ho: H1 = 2 H: H> H2 H: P

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Q2-Hi Bartleby team, I'm struggling with this general topic so please provide an answer and a short explanation for all the part of the exercise. Thanks in advance.

**Study on Treatment and Placebo Groups**

This analysis involves a study conducted using a treatment group and a placebo group. The results are presented in a table, and the study assumes that the two samples are independent simple random samples from normally distributed populations without assuming equal population standard deviations. The significance level used is 0.05.

### Table Summary
- **Treatment Group (μ₁)**
  - Sample size (n)= 27
  - Mean (x̄) = 2.31
  - Standard deviation (s) = 0.86

- **Placebo Group (μ₂)**
  - Sample size (n)= 39
  - Mean (x̄) = 2.67
  - Standard deviation (s) = 0.56

### Hypothesis Testing

**a. Test the claim that the two samples are from populations with the same mean.**

**Select the null and alternative hypotheses:**

- A. \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 > \mu_2 \)
- B. \( H_0: \mu_1 \neq \mu_2 \), \( H_1: \mu_1 < \mu_2 \)
- C. \( H_0: \mu_1 < \mu_2 \), \( H_1: \mu_1 \ge \mu_2 \)
- D. \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 \neq \mu_2 \)

**Calculate the following:**
- **Test statistic (t):** (Round to two decimal places as needed.)
- **P-value:** (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 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 sufficient evidence to warrant rejection of the
Transcribed Image Text:**Study on Treatment and Placebo Groups** This analysis involves a study conducted using a treatment group and a placebo group. The results are presented in a table, and the study assumes that the two samples are independent simple random samples from normally distributed populations without assuming equal population standard deviations. The significance level used is 0.05. ### Table Summary - **Treatment Group (μ₁)** - Sample size (n)= 27 - Mean (x̄) = 2.31 - Standard deviation (s) = 0.86 - **Placebo Group (μ₂)** - Sample size (n)= 39 - Mean (x̄) = 2.67 - Standard deviation (s) = 0.56 ### Hypothesis Testing **a. Test the claim that the two samples are from populations with the same mean.** **Select the null and alternative hypotheses:** - A. \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 > \mu_2 \) - B. \( H_0: \mu_1 \neq \mu_2 \), \( H_1: \mu_1 < \mu_2 \) - C. \( H_0: \mu_1 < \mu_2 \), \( H_1: \mu_1 \ge \mu_2 \) - D. \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 \neq \mu_2 \) **Calculate the following:** - **Test statistic (t):** (Round to two decimal places as needed.) - **P-value:** (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 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 sufficient evidence to warrant rejection of the
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