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? Patient 1 2 3 4 5 6 7   Total Blood Cholesterol (Before) 210 220 240 245 255 270 220   Total Blood Cholesterol​ (After) 203 216 241 242 251 269 216         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. Choose the correct answer below.     A. H0​: μd≥0 HA​: μd<0   B. H0​: μd=0 HA​: μd≠0   C. H0​: μd≤0 HA​: μd>0   D. H0​: μd≠0 HA​: μd=0 Calculate the standardized test statistic.   t=nothing ​(Round to three decimal places as​ needed.) Calculate the​ P-value.   ​P-value=nothing ​(Round to four decimal places as​ needed.) State the conclusion.   ▼   Fail to reject Reject H0. There ▼   is is not sufficient evidence to support the claim that the new cereal lowers total blood cholesterol levels.

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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?
Patient
1
2
3
4
5
6
7
 
Total Blood Cholesterol (Before)
210
220
240
245
255
270
220
 
Total Blood Cholesterol​ (After)
203
216
241
242
251
269
216
 
 
 
 
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.
Choose the correct answer below.
 
 
A.
H0​:
μd≥0
HA​:
μd<0
 
B.
H0​:
μd=0
HA​:
μd≠0
 
C.
H0​:
μd≤0
HA​:
μd>0
 
D.
H0​:
μd≠0
HA​:
μd=0
Calculate the standardized test statistic.
 
t=nothing
​(Round to three decimal places as​ needed.)
Calculate the​ P-value.
 
​P-value=nothing
​(Round to four decimal places as​ needed.)
State the conclusion.
 
 
Fail to reject
Reject
H0.
There
 
is
is not
sufficient evidence to support the claim that the new cereal lowers total blood cholesterol levels.
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