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 α=0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient 1 2 3 4 5 6 7 Total Blood Cholesterol (Before) 215 220 240 245 245 265 230 Total Blood Cholesterol (After) 209 219 241 243 244 262 229 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 μd=μ1−μ2. Choose the correct answer below. A. H0: μd=0 HA: μd≠0 B. H0: μd≠0 HA: μd=0 C. H0: μd≥0 HA: μd<0 D. H0: μd≤0 HA: μd>0 Calculate the standardized test statistic. t=nothing (Round to three decimal places as needed.) Calculate the P-value. P-value=nothing (Round to four decimal places as needed.) State the conclusion. Reject Fail to reject Reject H0. There is is not is sufficient evidence to support the claim that the new cereal lowers total blood cholesterol levels.

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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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

α=0.05,

can you conclude that the new cereal lowers total blood cholesterol levels?

Patient	1	2	3	4	5	6	7
Total Blood Cholesterol (Before)	215	220	240	245	245	265	230
Total Blood Cholesterol (After)	209	219	241	243	244	262	229

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

μd=μ1−μ2.

Choose the correct answer below.

H0:

μd=0

HA:

μd≠0

H0:

μd≠0

HA:

μd=0

H0:

μd≥0

HA:

μd<0

H0:

μd≤0

HA:

μd>0

Calculate the standardized test statistic.

t=nothing

(Round to three decimal places as needed.)

Calculate the P-value.

P-value=nothing

(Round to four decimal places as needed.)

State the conclusion.

Reject

Fail to reject

Reject

H0.

There

is not

sufficient evidence to support the claim that the new cereal lowers total blood cholesterol levels.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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