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Data on the weights (Ib) 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 0.05 significance level for both parts. Diet P1 40 0.78213 Ib 0.00435 Ib 0. a. lest the claim that the contents of cans of diet soda have weights with a mean that is less than the mean tor the regular soda. 0.0 What are the null and alternative hypotheses? OA Ho: H1 2 OB. Ho: H1 "P2 H: H H2 OC. Ho: H1=2 OD. Ho: H1 "2 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. Reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. O B. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. O C. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. O D. Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. b. Construct a confidence interval appropriate for the hypothesis test in part (a). (Round to three decimal places as needed.)

Data on the weights (Ib) 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 0.05 significance level for both parts. Diet P1 40 0.78213 Ib 0.00435 Ib 0. a. lest the claim that the contents of cans of diet soda have weights with a mean that is less than the mean tor the regular soda. 0.0 What are the null and alternative hypotheses? OA Ho: H1 2 OB. Ho: H1 "P2 H: H H2 OC. Ho: H1=2 OD. Ho: H1 "2 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. Reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. O B. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. O C. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. O D. Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. b. Construct a confidence interval appropriate for the hypothesis test in part (a). (Round to three decimal places as needed.)

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
Problem 1P
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### Statistical Analysis on Soda Weights #### Problem Scenario: You are tasked with analyzing the weights of diet soda cans compared to regular soda cans. The data, which considers independent simple random samples from normally distributed populations (with unequal population standard deviations), is summarized as follows: #### Data Summary: - **Diet Soda (μ₁):** - Sample size (n): 40 - Sample mean (x̄): 0.78213 lb - Sample standard deviation (s): 0.00435 lb - **Regular Soda (μ₂):** - Sample size (n): 40 - Sample mean (x̄): 0.81637 lb - Sample standard deviation (s): 0.00758 lb ### Hypothesis Testing: Using a significance level of 0.05, perform the following: #### Part (a): Hypothesis Testing Test the claim that the contents of diet soda cans have weights with a mean that is less than that for regular soda cans. - **Null and Alternative Hypotheses:** - Option A: \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 < \mu_2 \) - **Option B:** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 < \mu_2 \) - Option C: \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - Option D: \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \) - **Test Statistic:** - Compute \( t \)-value: \( \_\_\_ \) (Round to two decimal places) - **P-value:** - Compute the P-value: \( \_\_\_ \) (Round to three decimal places) - **Conclusion:** - Option A: Reject the null hypothesis. No sufficient evidence to support the diet soda cans having lower mean weights. - **Option B:** Fail to reject the null hypothesis. Sufficient evidence supports diet soda cans having lower mean weights. - Option C: Fail to reject
Transcribed Image Text:### Statistical Analysis on Soda Weights #### Problem Scenario: You are tasked with analyzing the weights of diet soda cans compared to regular soda cans. The data, which considers independent simple random samples from normally distributed populations (with unequal population standard deviations), is summarized as follows: #### Data Summary: - **Diet Soda (μ₁):** - Sample size (n): 40 - Sample mean (x̄): 0.78213 lb - Sample standard deviation (s): 0.00435 lb - **Regular Soda (μ₂):** - Sample size (n): 40 - Sample mean (x̄): 0.81637 lb - Sample standard deviation (s): 0.00758 lb ### Hypothesis Testing: Using a significance level of 0.05, perform the following: #### Part (a): Hypothesis Testing Test the claim that the contents of diet soda cans have weights with a mean that is less than that for regular soda cans. - **Null and Alternative Hypotheses:** - Option A: \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 < \mu_2 \) - **Option B:** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 < \mu_2 \) - Option C: \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - Option D: \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \) - **Test Statistic:** - Compute \( t \)-value: \( \_\_\_ \) (Round to two decimal places) - **P-value:** - Compute the P-value: \( \_\_\_ \) (Round to three decimal places) - **Conclusion:** - Option A: Reject the null hypothesis. No sufficient evidence to support the diet soda cans having lower mean weights. - **Option B:** Fail to reject the null hypothesis. Sufficient evidence supports diet soda cans having lower mean weights. - Option C: Fail to reject
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