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cted 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 est 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. at are the null and alternative hypotheses? A M₂: #₁ #₂ H₂: Hy

cted 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 est 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. at are the null and alternative hypotheses? A M₂: #₁ #₂ H₂: Hy

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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**Hypothesis Testing for Soda Can Weights** This lesson focuses on hypothesis testing to determine whether the mean weight of diet soda cans is less than that of regular soda cans, based on sample data. Assume two independent simple random samples from normally distributed populations and unequal population standard deviations. The significance level is 0.01. ### Data Summary | | Diet | Regular | |-----------|-------------|-------------| | Population Mean (μ) | \( \mu_1 \) | \( \mu_2 \) | | Sample Size (n) | 29 | 29 | | Sample Mean (\( \overline{x} \)) | 0.78858 lb | 0.80421 lb | | Sample Standard Deviation (s) | 0.00434 lb | 0.00749 lb | ### Part A: Hypothesis Testing We aim to test if the mean weight of diet soda is less than the mean weight of regular soda. #### Null and Alternative Hypotheses - **A.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 < \mu_2 \) - **B.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \) - **C.** \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 = \mu_2 \) - **D.** \( H_0: \mu_1 \ne \mu_2 \) \( H_1: \mu_1 \ne \mu_2 \) Select the correct pair: - **Selected Option:** A. \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 < \mu_2 \) #### Test Statistic - Compute the test statistic, \( t \). - **Test Statistic Value:** \( t = \_\_\_\_ \) (Round to two decimal places) #### P-Value - Determine the P-Value. - **P-Value:** \( P = \_\_\_\_\ \) (Round to three decimal places) #### Conclusion - Depending on the test result, you
Transcribed Image Text:**Hypothesis Testing for Soda Can Weights** This lesson focuses on hypothesis testing to determine whether the mean weight of diet soda cans is less than that of regular soda cans, based on sample data. Assume two independent simple random samples from normally distributed populations and unequal population standard deviations. The significance level is 0.01. ### Data Summary | | Diet | Regular | |-----------|-------------|-------------| | Population Mean (μ) | \( \mu_1 \) | \( \mu_2 \) | | Sample Size (n) | 29 | 29 | | Sample Mean (\( \overline{x} \)) | 0.78858 lb | 0.80421 lb | | Sample Standard Deviation (s) | 0.00434 lb | 0.00749 lb | ### Part A: Hypothesis Testing We aim to test if the mean weight of diet soda is less than the mean weight of regular soda. #### Null and Alternative Hypotheses - **A.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 < \mu_2 \) - **B.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \) - **C.** \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 = \mu_2 \) - **D.** \( H_0: \mu_1 \ne \mu_2 \) \( H_1: \mu_1 \ne \mu_2 \) Select the correct pair: - **Selected Option:** A. \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 < \mu_2 \) #### Test Statistic - Compute the test statistic, \( t \). - **Test Statistic Value:** \( t = \_\_\_\_ \) (Round to two decimal places) #### P-Value - Determine the P-Value. - **P-Value:** \( P = \_\_\_\_\ \) (Round to three decimal places) #### Conclusion - Depending on the test result, you
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