Question

In what follows use any of the following tests/procedures: Regression, multiple regression, confidence intervals, one sided T-test or two sided T-test. All the procedures should be done with 5% P-value or 95% confidence interval.Some answers are approximated, choose the most appropriate answer. SETUP: Is it reasonable to believe that people with body fat less than 20 (%) are of different height than the people with body fat of more than 20 (%). Given the data your job is to answer this question.

I. What test/procedure did you perform? (6.66 points)

• a. One sided T-test
• b. Two sided T-test
• c. Regression
• d. Confidence interval

II. Statistical interpretation? (6.66 points)

• a. Since P-value is small we are confident that the slope is not zero.
• b. Since P-value is small we are confident that the averages are different.
• c. Since P-value is too large the test is inconclusive.
• d. None of these.

III. Conclusion? (6.66 points)

• a. Yes, this is a reasonable belief.
• b. No, we cannot confirm that this is a reasonable belief.

BODYFAT	HEIGHT
12.9	67.75
6	72.25
25.5	66.25
10.6	72.25
28.1	71.25
20	74.75
19.2	69.75
11.9	72.5
4.3	74
12.9	73.5
7.6	74.5
8.3	76
20.4	69.5
19.8	71.25
22.2	69.5
20.9	66
28	71
23	71
15.6	67.75
16.9	73.5
18.5	68
15.5	69.75
14.7	68.25
18	70
13.6	67.75
4.3	71.5
8	67.5
22.4	67.5
4.4	64.75
8.9	69
13.2	73.75
6.3	71.25
12.6	71.25
21	71
31.9	73.5
39.1	65
23.2	70
26.6	68.25
34.3	72.25
32.1	67
32.3	68.75
31	29.5
31.1	70
29.9	71.5
8.1	68
14.9	73.25
10.5	67.5
6.1	71.25
14.4	68.5
4.1	66.75
11.1	72.25
7.6	69
8	67.75
7.8	73.5
5.4	67.5
22.3	72
20.5	68
26.8	69.5
29.7	70.75
24.1	65.75
25.4	73.25
28.2	68.5
29.4	70.25
25.5	67
30.3	70
29.7	67.5
20.5	70.75
13	71.5
7	69.25
12.6	71.5
24	71.5
8.8	68.75
9.5	73.75
14.2	64
11.5	65.75
19	67.5
8.6	69.5
21.1	68.5
20.6	70.25
18.8	69.25
30	67.75
26.2	67.25
18.7	72.75
25.4	70
26.1	69.25
26.1	67.5
15.9	67.25
23.2	65.75
8.9	72.5
14.8	73
20.4	70
18.4	69.5
9.4	70.5
25	71.75
9.5	74.5
16.4	77.75
9.8	73.25
11.8	66.5
18.2	68.25
22.5	72
20.1	73.5
20.7	72
19.2	71.25
21.7	73.75
25	69.25
18.7	68.5
18.5	73.5
19	74.25
16.9	75.5
20.4	69.25
19.6	68.5
26.5	70
22	70
20.8	70.25
26.1	71.75
15.9	69.25
19	72.75
14.7	72
24.2	74
18.2	72.25
26.9	74.5
24.9	71.5
15.2	68.75
16.4	66.75
13.5	66.5
17.4	67
26.6	68.75
17.1	67.75
20	73.25
15.5	69.75
18.9	71.5
22.8	70.5
22.1	73.25
24.4	66.75
23.3	69.5
26.1	69.75
21.8	70.75
28.6	74
21.8	71.25
20.8	75
24.9	71
17.5	69.5
22.7	67.75
9.3	72.25
10.2	77.5
13.9	70.75
19.6	72.75
27.8	69.75
6.1	72.5
25.2	70.25
9.3	69
19.1	74.5
10.2	72.25
16.6	67.25
21.3	73.5
16.9	75.25
30.6	69
10.3	72.25
12.1	68.75
22.5	71.5
10.6	72.25
14.5	73
13.4	68.75
15.5	70.5
26.4	72
18	73.75
21.4	68
19.5	72.25
35.3	69.5
15.5	69.5
3.8	67.75
1.4	65.5
19.5	71
16.8	71.5
24.4	71.75
11	69.25
12.8	67
29.7	71.5
21.6	69.25
16.7	74.5
26.7	74.25
0	68
12.1	67.25
11.7	69.75
16.8	74.25
9.5	71.5
22.5	74.25
19.2	72
19.6	72.5
24.5	68.25
11.6	69.25
36.8	76
16.8	70.5
23.1	74.75
22.8	72.75
24.3	68.25
21.5	69
18.6	71.5
7.4	72.75
22.3	67.5
11.8	70.25
20.9	69.25
27.6	71.5
6.7	74
33.8	69.75
16.5	73
31.7	65.5
31.8	72.5
9.7	70.25
10.9	70.75
7.8	68
26.1	74.5
18.7	71.75
18.6	70.75
19	73
45.1	64
13.3	69.75
8.2	70
23	71.75
16	69.25
11.9	70.5
24.9	72.25
12	67.5
6.7	67.25
11.6	68.75
13.3	66.75
14	68.25
23.7	74.25
15.6	69.5
16.3	68.5
12.1	65.75
15.7	71.75
16.4	71.5
25.3	67.25
26.2	67.5
18.4	67.5
23.9	72.25
26.1	69.5
13.5	69.5
28.8	65.75
16.3	65.75
33.4	68.25
28.5	72
31.7	72.75
28.7	68.5
15.6	69.25
29	70.5
12.5	67
33	69.75
27.9	66
24.5	70.5
29.9	70

Answer 1

The given research question is

"Is it reasonable to believe that people with body fat less than 20 (%) are of different height than the people with body fat of more than 20 (%)."

The above statement is a non directional statement.

The hypothesis will be

considering mu1 be the population mean people with body fat less than 20 (%) and mu2 be the population mean people with body fat more than 20 (%)

I. What test/procedure did you perform? (6.66 points)

Two sided T-test

II) I have not considered two observations which are 20% fat because we have to compare < 20% and >20% fat.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
HEIGHT (fat<20%)	139	70.37	2.70	0.23
HEIGHT (fat>20%)	111	69.80	4.59	0.44

= 3.657

test statistic t = = 1.213

p-value = 0.2263

p-value is more than 0.05 we fail to reject null hypothesis and there is no significant evidence to conclude that people with body fat less than 20 (%) are of different height than the people with body fat of more than 20 (%).

II. Statistical interpretation? (6.66 points)

• c. Since P-value is too large the test is inconclusive.

III. Conclusion? (6.66 points)

• b. No, we cannot confirm that this is a reasonable belief.