identify the test statistic, p value, and confidence interval ### Comparison of Diet Soda and Regular Soda Can Weights**Data Description:**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 in the table below. The samples are independent simple random samples selected from normally distributed populations. It is assumed that the population standard deviations are not equal. We will use a 0.01 significance level for our tests.**| Parameter | Diet (μ₁) | Regular (μ₂) ||-----------|-----------|--------------|| Sample Size (n) | 32 | 32 || Sample Mean (x̄) | 0.78993 lb | 0.81209 lb || Sample Standard Deviation (s) | 0.00437 lb | 0.00748 lb |### Part (a): Hypothesis Testing - Comparison of Means**Objective:**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.**Hypotheses:**- **Null Hypothesis (H₀):** μ₁ = μ₂ - This suggests that the average weight of the contents of diet soda cans is equal to that of regular soda cans.- **Alternative Hypothesis (Hₐ):** μ₁ < μ₂ - This suggests that the average weight of the contents of diet soda cans is less than that of regular soda cans.### Next Steps: - Calculate the test statistic using the sample data.- Compare the test statistic to the critical value for the 0.01 significance level.- Draw a conclusion based on this comparison.This structured approach will help you determine whether to reject the null hypothesis in favor of the alternative hypothesis, thereby supporting the claim that diet soda cans weigh less on average compared to regular soda cans.

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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 0.01 significance level for both parts. Diet Regular 42 32 32 X 0.78993 lb 0.81209 lb 0.00437 lb. 0.00748 lb

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 0.01 significance level for both parts. Diet Regular 42 32 32 X 0.78993 lb 0.81209 lb 0.00437 lb. 0.00748 lb

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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

identify the test statistic, p value, and confidence interval

### Comparison of Diet Soda and Regular Soda Can Weights

**Data Description:**
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 in the table below. The samples are independent simple random samples selected from normally distributed populations. It is assumed that the population standard deviations are not equal. We will use a 0.01 significance level for our tests.

**

| Parameter | Diet (μ₁) | Regular (μ₂) |
|-----------|-----------|--------------|
| Sample Size (n) | 32 | 32 |
| Sample Mean (x̄) | 0.78993 lb | 0.81209 lb |
| Sample Standard Deviation (s) | 0.00437 lb | 0.00748 lb |

### Part (a): Hypothesis Testing - Comparison of Means

**Objective:**
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.

**Hypotheses:**

- **Null Hypothesis (H₀):** μ₁ = μ₂
- This suggests that the average weight of the contents of diet soda cans is equal to that of regular soda cans.
- **Alternative Hypothesis (Hₐ):** μ₁ < μ₂
- This suggests that the average weight of the contents of diet soda cans is less than that of regular soda cans.

### Next Steps:

- Calculate the test statistic using the sample data.
- Compare the test statistic to the critical value for the 0.01 significance level.
- Draw a conclusion based on this comparison.

This structured approach will help you determine whether to reject the null hypothesis in favor of the alternative hypothesis, thereby supporting the claim that diet soda cans weigh less on average compared to regular soda cans.

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