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

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.

Homework Answers

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.

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