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 Diet Regular 35 35 0.79744 lb 0.81745 lb parts. 0.00443 lb 0.00749 lb 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?

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 Diet Regular 35 35 0.79744 lb 0.81745 lb parts. 0.00443 lb 0.00749 lb 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?

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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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

find the test statistic, p value, and confidence interval

### Weight Comparison of Diet Soda vs. Regular Soda

**Introduction:**
This study aims to analyze and compare the weights (in pounds) of the contents of diet soda cans versus those of regular soda cans. We assume that the two samples are independent simple random samples selected from normally distributed populations, and we do not assume that the population standard deviations are equal. The significance level for this study is set at 0.01.

**Data Summary:**

| | Diet | Regular |
|------|------------------|------------------|
| μ | μ₁ | μ₂ |
| n | 35 | 35 |
| x̄ | 0.79744 lb | 0.81745 lb |
| s | 0.00443 lb | 0.00749 lb |

Where:
- $ μ $ denotes the population mean
- $ n $ denotes the sample size
- $ x̄ $ denotes the sample mean
- $ s $ denotes the sample standard deviation

#### a. Hypothesis Testing:

We need 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.

**Null and Alternative Hypotheses:**

- **Null Hypothesis (H₀)**: μ₁ = μ₂ (The mean weight of the contents of diet soda cans is the same as the mean weight of the contents of regular soda cans)

- **Alternative Hypothesis (H₁)**: μ₁ < μ₂ (The mean weight of the contents of diet soda cans is less than the mean weight of the contents of regular soda cans)

To test this hypothesis, we will use an appropriate statistical test (such as a t-test for unequal variances) given the data provided, the assumptions of normality, and the significance level of 0.01. The decision to reject or fail to reject the null hypothesis will be based on the p-value obtained from the test in comparison to the significance level.

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