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

PatientPatient	1	2	3	4	5	6	7
Total Blood Cholesterol (Before)	210	225	235	250	240	260	235
Total Blood Cholesterol​ (After)	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.

Answer 1

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.