You wish to compare how a lowfat diet lowfat diet and a bris

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

M_lfd = 10

8

64

n_lfd = 6

15

225

12

144

9

81

6

36

?X_lfd = 60

?X2 = 650

Diet + Walk

14

196

M_dietwalk = 15

12

144

n_dietwalk = 6

18

324

16

256

13

169

17

289

?X_dietwalk = 90

?X2 = 1378

Diet + Run

19

361

M_dietrun = 17

15

225

n_dietrun = 6

14

196

16

256

18

324

20

400

?X_dietrun = 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

Solution

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Make Assumptions and meet test requirements.

All assmuption meet test requirements.

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State the null hypothesis.

Null hypothesis: all means are equal

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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.

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Compute the test statistic.

F=11.04

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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	Total