You wish to compare how a low-fat diet, low-fat diet and a brisk four-mile walk
ID: 3432172 • Letter: Y
Question
You wish to compare how a low-fat diet, low-fat diet and a brisk four-mile walk each day, and a low-fat diet and a four-mile job each day affect cholesterol levels. You randomly assign six subjects to each group. The scores in the table below show the reduction in cholesterol count after two months.
Conduct all 5 steps of the appropriate statistic. Be sure to label all five steps.
Report the statistics as you would in a journal article.
Low-Fat Diet
Diet and Walk
Diet and Run
10
14
19
8
12
15
15
18
14
12
16
16
9
13
18
6
17
20
Make Assumptions and meet test requirements.
State the null hypothesis.
Select the sampling distribution and establish the critical region.
Compute the test statistic.
Sample
X
X2
Low-fat diet
10
100
Mlfd = 10
8
64
nlfd = 6
15
225
12
144
9
81
6
36
?Xlfd = 60
?X2 = 650
Diet + Walk
14
196
Mdietwalk = 15
12
144
ndietwalk = 6
18
324
16
256
13
169
17
289
?Xdietwalk = 90
?X2 = 1378
Diet + Run
19
361
Mdietrun = 17
15
225
ndietrun = 6
14
196
16
256
18
324
20
400
?Xdietrun = 102
?X2 = 1762
Summary Data Table
Low-fat
Diet+Walk
Diet+Run
?X
60
90
102
?X2
650
1378
1762
Group Mean
10
15
17
Grand Mean
14
Source Table
Source
SS
df
MS
F
Between-Groups
?
?
?
?
Within-Groups
?
15
?
Total
?
17
SST = ?X2
Low-Fat Diet
Diet and Walk
Diet and Run
10
14
19
8
12
15
15
18
14
12
16
16
9
13
18
6
17
20
Explanation / Answer
------------------------------------------------------------------------------------------------------
Make Assumptions and meet test requirements.
All assmuption meet test requirements.
------------------------------------------------------------------------------------------------------
State the null hypothesis.
Null hypothesis: all means are equal
------------------------------------------------------------------------------------------------------
Select the sampling distribution and establish the critical region.
The sampling distribution is F distribution
Assume that the significant level a=0.05
The ciritical value is F(0.95, df1=2, df2=15) =3.68 (from F table)
So the critical region is if F>3.68, we reject the null hypothesis.
------------------------------------------------------------------------------------------------------
Compute the test statistic.
F=11.04
------------------------------------------------------------------------------------------------------
Make a decision and interpret results.
Since F=11.04 is larger than 3.68, we reject the null hypothesis. So we can conclude that
at least one mean is different.
Mean n Std. Dev 10.0 6 3.16 Low-Fat Diet 15.0 6 2.37 Diet and Walk 17.0 6 2.37 Diet and Run 14.0 18 3.93 TotalRelated Questions
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