A food manufacturer claims that eating its new cereal as part of a daily diet lo
ID: 3314784 • Letter: A
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 =0.05 can you conclude that the new cereal lowers total blood cholesterol levels?
a) calculate the test statistic T = b) find the P value C) (fail to reject / reject) H0. There ( is / is not) sufficient evidence to support the claim that the new cereal lowers total blood cholesterol levels.
Patient
1
2
3
4
5
6
7
Total Blood Cholesterol left parenthesis Before right parenthesisTotal Blood Cholesterol (Before)
205
230
235
240
245
265
220
Total Blood Cholesterol (After)
196
22
238
236
243
264
218
Patient
1
2
3
4
5
6
7
Total Blood Cholesterol left parenthesis Before right parenthesisTotal Blood Cholesterol (Before)
205
230
235
240
245
265
220
Total Blood Cholesterol (After)
196
22
238
236
243
264
218
Explanation / Answer
Given that,
null, H0: Ud = 0
alternate, H1: Ud < 0
level of significance, = 0.05
from standard normal table,left tailed t /2 =2.015
since our test is left-tailed
reject Ho, if to < -2.015
we use Test Statistic
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 36.833
We have d = 36.833
pooled variance = calculate value of Sd= S^2 = sqrt [ 43375-(221^2/6 ] / 5 = 83.946
to = d/ (S/n) = 1.075
critical Value
the value of |t | with n-1 = 5 d.f is 2.015
we got |t o| = 1.075 & |t | =2.015
make Decision
hence Value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < 1.0748 ) = 0.83421
hence value of p0.05 < 0.83421,here we do not reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud < 0
test statistic: 1.075
critical value: reject Ho, if to < -2.015
decision: Do not Reject Ho
p-value: 0.83421
we do not have enough evidence to support the claim that the new cereal lowers total blood cholesterol levels
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