**Cholesterol Level Study for Cereal Diet Impact**A food manufacturer asserts that incorporating its new cereal into a daily diet reduces total blood cholesterol levels. This study examines total blood cholesterol levels (in milligrams per deciliter of blood) in seven patients, both before and after one year of including the cereal in their diet.### Cholesterol Levels Table:| Patient | Total Blood Cholesterol (Before) | Total Blood Cholesterol (After) ||---------|----------------------------------|---------------------------------|| 1 | 215 | 205 || 2 | 225 | 224 || 3 | 240 | 244 || 4 | 240 | 236 || 5 | 240 | 238 || 6 | 270 | 267 || 7 | 220 | 216 |**Assumptions:**- Samples are random and dependent.- Population is normally distributed.**Hypothesis Testing:**Using a significance level (\(\alpha = 0.05\)), we aim to determine if the cereal significantly lowers cholesterol. The difference in means, \(\mu_d = \mu_1 - \mu_2\), is tested.**Hypotheses Options:**- **A.** \( H_0: \mu_d \geq 0 \) and \( H_A: \mu_d < 0 \)- **B.** \( H_0: \mu_d = 0 \) and \( H_A: \mu_d \neq 0 \)- **C.** \( H_0: \mu_d \neq 0 \) and \( H_A: \mu_d = 0 \)- **D.** \( H_0: \mu_d \leq 0 \) and \( H_A: \mu_d > 0 \) (Chosen)**Statistical Calculation:**Calculate the standardized test statistic \( t \). (Round to three decimal places as needed.)---This educational example demonstrates how to conduct dependent sample hypothesis testing to evaluate dietary changes and analyze implications for health.

Solution: First we find sample mean and standard deviation for the difference score. Before After d=Before -After (d-d)2 215 205 10 51.02041 225 224 1 3.44898 240 244 -4 47.02041 240 236 4 1.306122 240 238 2 0.734694 270 267 3 0.020408 220 216 4 1.306122 n=7 Sample sized =∑dn=207=2.8571sd=∑(d-d)2n-1sd=104.85716sd=4.180453Test statistic t=dsd/nt=2.85714.180453/7t=2.85711.580063=1.808219t=1.808 The value of the standardized test statistic is 1.808

Math

Statistics

A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. T table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating th 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 x = 0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient Total Blood Cholesterol (Before) Total Blood Cholesterol (After) 1 215 205 2 225 224 3 240 244 4 240 236 5 240 238 6 270 267 7 220 216 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.

A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. T table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating th 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 x = 0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient Total Blood Cholesterol (Before) Total Blood Cholesterol (After) 1 215 205 2 225 224 3 240 244 4 240 236 5 240 238 6 270 267 7 220 216 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.

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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