Question

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 αs=0.05 , can you conclude that the new cereal lowers total blood cholesterol levels?

Before	After
205	203
220	215
235	240
240	239
245	242
270	268
220	218

μd=μ1−μ2.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

Calculate the standardized test statistic.

Calculate the P-value.

State the conclusion.

Answer 1

The statistical software output for this problem is;

Hence,

Standardized test statistic = 1.219

P - value = 0.1344

Conclusion: Since p - value is greater than 0.05, we fail to reject Ho. Hence,

There is not enough evidence to support the claim that the new cereal lowers total blood cholesterol levels.