Regular 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 H2 23 23 0.79113 lb 0.81882 Ib 0.00435 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? O A. Ho: H1#H2 H: P1 < H2 O B. Hg: H1 = P2 OC. Ho: H1 = H2 O D. Ho: H1 = H2 H1: 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. CA. 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 B. 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. CC. 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 D. 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.
Regular 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 H2 23 23 0.79113 lb 0.81882 Ib 0.00435 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? O A. Ho: H1#H2 H: P1 < H2 O B. Hg: H1 = P2 OC. Ho: H1 = H2 O D. Ho: H1 = H2 H1: 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. CA. 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 B. 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. CC. 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 D. 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.
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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Q1A- Hi Bartleby team, I'm struggling with this general topic so please provide an answer and a short explanation for this part. Thanks in advance.
![**Title: Comparative Analysis of Diet and Regular Soda Can Weights**
**Overview:**
This educational section presents a statistical analysis comparing the weight of contents in cans of diet soda to those in regular soda. The analysis assumes two independent simple random samples from normally distributed populations without assuming equal population standard deviations. A significance level of 0.05 is used.
**Data Table:**
| | Diet (\(\mu_1\)) | Regular (\(\mu_2\)) |
|-------------|--------------|----------------|
| Sample size (\(n\)) | 23 | 23 |
| Sample mean (\(\bar{x}\)) | 0.79113 lb | 0.81882 lb |
| Sample standard deviation (\(s\)) | 0.00435 lb | 0.00749 lb |
**Hypothesis Testing:**
- **Research Question:** Test the claim that cans of diet soda have weights with a mean less than that of regular soda.
- **Null and Alternative Hypotheses Options:**
- A. \(H_0: \mu_1 \neq \mu_2\); \(H_1: \mu_1 < \mu_2\)
- B. \(H_0: \mu_1 = \mu_2\); \(H_1: \mu_1 < \mu_2\)
- C. \(H_0: \mu_1 = \mu_2\); \(H_1: \mu_1 > \mu_2\)
- D. \(H_0: \mu_1 = \mu_2\); \(H_1: \mu_1 \neq \mu_2\)
**Answers:**
- **Test Statistic (t):** [Value to be calculated and rounded to two decimal places]
- **P-Value:** [Value to be calculated and rounded to three decimal places]
**Conclusion Options:**
- A. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that diet soda cans have lower mean weights than regular soda.
- B. Reject the null hypothesis. There is not sufficient evidence to support the claim that diet soda cans have lower mean weights than regular soda.
- C. Reject the null hypothesis. There is sufficient evidence to support the claim that diet soda cans have lower mean weights than regular soda.
- D. Fail](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22c22731-3858-419d-b4a1-f1d81ff5f2b6%2F2b458ae6-7b6a-48d2-82b0-e0c8bd7c8205%2F45m9xn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Comparative Analysis of Diet and Regular Soda Can Weights**
**Overview:**
This educational section presents a statistical analysis comparing the weight of contents in cans of diet soda to those in regular soda. The analysis assumes two independent simple random samples from normally distributed populations without assuming equal population standard deviations. A significance level of 0.05 is used.
**Data Table:**
| | Diet (\(\mu_1\)) | Regular (\(\mu_2\)) |
|-------------|--------------|----------------|
| Sample size (\(n\)) | 23 | 23 |
| Sample mean (\(\bar{x}\)) | 0.79113 lb | 0.81882 lb |
| Sample standard deviation (\(s\)) | 0.00435 lb | 0.00749 lb |
**Hypothesis Testing:**
- **Research Question:** Test the claim that cans of diet soda have weights with a mean less than that of regular soda.
- **Null and Alternative Hypotheses Options:**
- A. \(H_0: \mu_1 \neq \mu_2\); \(H_1: \mu_1 < \mu_2\)
- B. \(H_0: \mu_1 = \mu_2\); \(H_1: \mu_1 < \mu_2\)
- C. \(H_0: \mu_1 = \mu_2\); \(H_1: \mu_1 > \mu_2\)
- D. \(H_0: \mu_1 = \mu_2\); \(H_1: \mu_1 \neq \mu_2\)
**Answers:**
- **Test Statistic (t):** [Value to be calculated and rounded to two decimal places]
- **P-Value:** [Value to be calculated and rounded to three decimal places]
**Conclusion Options:**
- A. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that diet soda cans have lower mean weights than regular soda.
- B. Reject the null hypothesis. There is not sufficient evidence to support the claim that diet soda cans have lower mean weights than regular soda.
- C. Reject the null hypothesis. There is sufficient evidence to support the claim that diet soda cans have lower mean weights than regular soda.
- D. Fail
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