### Analysis of Soda Can Weights: Diet vs. RegularOn this educational page, we analyze the weights (in pounds) of the contents of cans of diet soda compared to those of regular soda. The data for this analysis is summarized below. 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. The analysis is conducted with a 0.01 significance level.#### Summary DataThe table below summarizes the sample data:| | Diet Soda | Regular Soda ||------------------------|-------------------|-------------------|| Population Mean (μ) | $\mu_1$ | $\mu_2$ || Sample Size (n) | 29 | 29 || Sample Mean (x̄) | 0.79133 lb | 0.80866 lb || Sample Standard Dev (s)| 0.00444 lb | 0.00752 lb |### Hypothesis Testing#### Part (a)We need to determine whether we should reject the null hypothesis, which states that there is no difference in the mean weights between diet and regular soda cans, for the following claim:"The cans of diet soda have mean weights that are lower than the mean weights of the regular soda."**Options for Conclusion:**- **A.** 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.** 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.- **C.** 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.- **D.** 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.The correct conclusion, based on the given data and a 0.01 significance level, is:- **Option B:** 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 ### Comparison of Diet Soda versus Regular Soda Contents Weight#### Hypothesis Testing OverviewWe aim to 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. The data obtained from the samples is shown below, along with the steps to perform in hypothesis testing.#### Sample DataA summary of the sample data is presented in the table below:| Parameter | Diet (µ₁) | Regular (µ₂) ||-----------|------------------|------------------|| $ n $ | 29 | 29 || $ \bar{x} $ | 0.79133 lb | 0.80866 lb || $ s $ | 0.00444 lb | 0.00752 lb |Here:- $ n $ is the sample size.- $ \bar{x} $ is the sample mean.- $ s $ is the sample standard deviation.#### Hypothesis Formation**Null and Alternative Hypotheses:**The hypothesis test to determine if the mean weight of diet soda cans is less than that of regular soda cans can be stated as:- Null Hypothesis (H₀): $ \mu₁ = \mu₂ $- Alternative Hypothesis (H₁): $ \mu₁ < \mu₂ $#### Test StatisticsThe test statistic $ t $:\[ t = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\left( \frac{s_1^2}{n_1} \right) + \left( \frac{s_2^2}{n_2} \right)}} \]- $ \bar{x}_1 $ = 0.79133 lb- $ \bar{x}_2 $ = 0.80866 lb- $ s_1 $ = 0.00444 lb- $ s_2 $ = 0.00752 lb- $ n_1 $ = 29- $ n_2 $ = 29\[ \text{Substitute the values to find } t. \]\[ t = \boxed{} \]#### P-ValueThe P-Value helps in determining the significance of the results from the test statistic:\[ \text{P-Value} =

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Description: ### Analysis of Soda Can Weights: Diet vs. RegularOn this educational page, we analyze the weights (in pounds) of the contents of cans of diet soda compared to those of regular soda. The data for this analysis is summarized below. Assume that the tw

Given Data : Null and Alternative Hypotheses The claim : The cans of diet soda have lower mean…

Math

Statistics

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? O A. Ho Hi= H2 O B. Ho H P2 O D. Ho Hi =P2 O C. Ho H, =H2 H 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. A. 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

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? O A. Ho Hi= H2 O B. Ho H P2 O D. Ho Hi =P2 O C. Ho H, =H2 H 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. A. 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

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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