A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At a=0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient 1 Total Blood Cholesterol (Before) Total Blood Cholesterol (After) O A. Ho: Hd #0 HA: Hd=0 OC. Ho: Hd = 0 HA: Hd #0 Calculate the standardized test statistic. t= (Round to three decimal places as needed.) Calculate the P-value.. P-value = (Round to four decimal places as needed.) State the conclusion. Ho. There W 205 197 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where Hd ₁-₂. Choose the correct answer below. s EITB 2 230 228 OB. Ho Hd 20 HA: Hd <0 3 235 237 OD. Ho: Hd ≤0 HA: Hd>0 4 240 238 5 255 254 sufficient evidence to support the claim that the new cereal lowers total blood cholesterol levels. 6 260 259 7 230 225
A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At a=0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient 1 Total Blood Cholesterol (Before) Total Blood Cholesterol (After) O A. Ho: Hd #0 HA: Hd=0 OC. Ho: Hd = 0 HA: Hd #0 Calculate the standardized test statistic. t= (Round to three decimal places as needed.) Calculate the P-value.. P-value = (Round to four decimal places as needed.) State the conclusion. Ho. There W 205 197 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where Hd ₁-₂. Choose the correct answer below. s EITB 2 230 228 OB. Ho Hd 20 HA: Hd <0 3 235 237 OD. Ho: Hd ≤0 HA: Hd>0 4 240 238 5 255 254 sufficient evidence to support the claim that the new cereal lowers total blood cholesterol levels. 6 260 259 7 230 225
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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![### Does New Cereal Lower Total Blood Cholesterol Levels?
**Background**: A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table provided shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. We will use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At a significance level of \( \alpha = 0.05 \), can we conclude that the new cereal lowers total blood cholesterol levels?
#### Data Table
| Patient | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|------------------------|-----|-----|-----|-----|-----|-----|-----|
| Total Blood Cholesterol (Before) | 205 | 230 | 235 | 240 | 255 | 260 | 230 |
| Total Blood Cholesterol (After) | 197 | 228 | 237 | 238 | 254 | 259 | 225 |
#### Hypothesis Testing
Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where \( \mu_d = \mu_1 - \mu_2 \). Choose the correct answer below:
- **A. \[ H_0: \mu_d \ne 0 \] \[ H_A: \mu_d = 0 \]**
- **B. \[ H_0: \mu_d \ge 0 \] \[ H_A: \mu_d < 0 \]**
- **C. \[ H_0: \mu_d = 0 \] \[ H_A: \mu_d \ne 0 \]**
- **D. \[ H_0: \mu_d \le 0 \] \[ H_A: \mu_d > 0 \]**
#### Calculations
1. **Calculate the Standardized Test Statistic**:
\[ t = \_\_\_ \]
*(Round to three decimal places as needed.)*
2. **Calculate the P-Value**:
\[ P\text{-value} = \_\_\_ \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c71094c-6a42-4b2e-b93a-0f0d489253a3%2F781cc668-1bef-4bd6-925b-742de50ac879%2Fgqt0abl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Does New Cereal Lower Total Blood Cholesterol Levels?
**Background**: A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table provided shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. We will use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At a significance level of \( \alpha = 0.05 \), can we conclude that the new cereal lowers total blood cholesterol levels?
#### Data Table
| Patient | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|------------------------|-----|-----|-----|-----|-----|-----|-----|
| Total Blood Cholesterol (Before) | 205 | 230 | 235 | 240 | 255 | 260 | 230 |
| Total Blood Cholesterol (After) | 197 | 228 | 237 | 238 | 254 | 259 | 225 |
#### Hypothesis Testing
Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where \( \mu_d = \mu_1 - \mu_2 \). Choose the correct answer below:
- **A. \[ H_0: \mu_d \ne 0 \] \[ H_A: \mu_d = 0 \]**
- **B. \[ H_0: \mu_d \ge 0 \] \[ H_A: \mu_d < 0 \]**
- **C. \[ H_0: \mu_d = 0 \] \[ H_A: \mu_d \ne 0 \]**
- **D. \[ H_0: \mu_d \le 0 \] \[ H_A: \mu_d > 0 \]**
#### Calculations
1. **Calculate the Standardized Test Statistic**:
\[ t = \_\_\_ \]
*(Round to three decimal places as needed.)*
2. **Calculate the P-Value**:
\[ P\text{-value} = \_\_\_ \]
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