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
210	202
230	226
225	226
240	239
245	241
265	261
220	219

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.

Calculate the standardized test statistic.

Calculate the P-value.

State the conclusion.

Answer 1

The statistical software output for this problem is:

Hence,

Test statistic = 2.696

P - value = 0.0358

Conclusion: Since p - value is less than 0.05, we reject the null hypothesis. Hence,

We have sufficient evidence to conclude that the new cereal lowers total blood cholesterol levels.