MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Effect of New Cereal on Total Blood Cholesterol Levels A food manufacturer claims that incorporating its new cereal into a daily diet can lower total blood cholesterol levels. To verify this claim, data were collected from seven patients before and after one year of consuming the cereal as part of their diets. The table below provides the total blood cholesterol levels (in milligrams per deciliter of blood) for each patient: | Patient | Total Blood Cholesterol (Before) | Total Blood Cholesterol (After) | |---------|----------------------------------|---------------------------------| | 1 | 200 | 196 | | 2 | 230 | 227 | | 3 | 240 | 245 | | 4 | 240 | 236 | | 5 | 245 | 243 | | 6 | 260 | 255 | | 7 | 225 | 223 | ### Hypothesis Testing To assess whether the new cereal effectively lowers blood cholesterol levels, we define the following: - Population 1: Blood cholesterol levels before eating the cereal. - Population 2: Blood cholesterol levels after eating the cereal. We set up our null and alternative hypotheses as follows: - Null Hypothesis (H₀): μ_d ≤ 0 (The mean difference in cholesterol levels before and after consuming the cereal is less than or equal to zero, indicating no decrease or an increase in cholesterol levels.) - Alternative Hypothesis (Hₐ): μ_d > 0 (The mean difference in cholesterol levels before and after consuming the cereal is greater than zero, indicating a decrease in cholesterol levels.) The correct answer is **C**. ### Calculation of the Standardized Test Statistic We need to calculate the standardized test statistic (t) to determine whether the observed data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. \[ t = \text{(formula here)} \] **(The actual formula and calculation steps were not provided; hence it's indicated with a placeholder for detailed calculations.)** **Note:** The t-value should be rounded to three decimal places as needed. In summary, this analysis involves testing whether the new cereal has a significant effect on lowering total blood cholesterol levels, based on the provided patient data and defined hypotheses.
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Transcribed Image Text:### Effect of New Cereal on Total Blood Cholesterol Levels A food manufacturer claims that incorporating its new cereal into a daily diet can lower total blood cholesterol levels. To verify this claim, data were collected from seven patients before and after one year of consuming the cereal as part of their diets. The table below provides the total blood cholesterol levels (in milligrams per deciliter of blood) for each patient: | Patient | Total Blood Cholesterol (Before) | Total Blood Cholesterol (After) | |---------|----------------------------------|---------------------------------| | 1 | 200 | 196 | | 2 | 230 | 227 | | 3 | 240 | 245 | | 4 | 240 | 236 | | 5 | 245 | 243 | | 6 | 260 | 255 | | 7 | 225 | 223 | ### Hypothesis Testing To assess whether the new cereal effectively lowers blood cholesterol levels, we define the following: - Population 1: Blood cholesterol levels before eating the cereal. - Population 2: Blood cholesterol levels after eating the cereal. We set up our null and alternative hypotheses as follows: - Null Hypothesis (H₀): μ_d ≤ 0 (The mean difference in cholesterol levels before and after consuming the cereal is less than or equal to zero, indicating no decrease or an increase in cholesterol levels.) - Alternative Hypothesis (Hₐ): μ_d > 0 (The mean difference in cholesterol levels before and after consuming the cereal is greater than zero, indicating a decrease in cholesterol levels.) The correct answer is **C**. ### Calculation of the Standardized Test Statistic We need to calculate the standardized test statistic (t) to determine whether the observed data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. \[ t = \text{(formula here)} \] **(The actual formula and calculation steps were not provided; hence it's indicated with a placeholder for detailed calculations.)** **Note:** The t-value should be rounded to three decimal places as needed. In summary, this analysis involves testing whether the new cereal has a significant effect on lowering total blood cholesterol levels, based on the provided patient data and defined hypotheses.
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