Question

# A food manufacturer claims that eating its new cereal as part of a daily diet lowers...

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?

 PatientPatient Total Blood Cholesterol (Before) Total Blood Cholesterol​ (After) 1 2 3 4 5 6 7 210 225 235 250 240 260 235 200 224 240 245 239 258 234

calculate the test statistic

find the P value

(fail to reject / reject) H0. There ( is / is not) sufficient evidence to support the claim that the new cereal lowers total blood cholesterol levels.

To Test :-

H0 :-

H1 :-

 Number Before After Difference 210 200 10 61.7346939 225 224 1 1.30612245 235 240 -5 51.0204082 250 245 5 8.16326531 240 239 1 1.30612245 260 258 2 0.02040816 235 234 1 1.30612245 Total 1655 1640 15 124.857143

Test Statistic :-

t = 1.2428

Test Criteria :-
Reject null hypothesis if

Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.5251 ) = 0.1337
Reject null hypothesis if P value < level of significance
P - value = 0.1337 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that the new cereal lowers total blood cholesterol​ levels at 5% level of significance.

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