Question

An experiment sought to discover if a course on nutrition would influence the Body Mass Index (BMI) of the students enrolled. Measures of body fat percentages were taken before the yearlong course and then again at the end of the course for each of the 10 students. The data are as follows: Student: 1 2 3 4 5 6 7 8 9 10 Before: 16.85 18.62 35.79 22.66 18.74 22.25 19.95 14.61 27.49 20.00 End: 16.42 18.53 36.01 22.53 18.59 22.03 19.25 14.06 26.11 19.42 Test the hypothesis at the 0.05 level of significance that the mean body fat percentages of the students decreased by the end of the course. Solve using MegaStat

Answer 1

Null hypothesis H₀: The mean body fat percentages of the students at the end of the course is greater than or equal to the mean body fat percenterage of the students at starting of the course.

Alternate hypothesis H₁:The mean body fat percentages of the students at the end of the course is lesser than the mean body fat percenterage of the students at starting of the course.

Test and Test statistic: As the samples are dependent, the appropriate test is the paired-t test and the test statistic for the test is as follows.

The following table is the inputs for Megastat

Student	Before	After
1	16.85	16.42
2	18.62	18.53
3	35.79	36.01
4	22.66	22.53
5	18.74	18.59
6	22.25	22.03
7	19.95	19.25
8	14.61	14.06
9	27.49	26.11
10	20	19.42

Select - Megastat Addin

Hypothesis tests

Paired Observations

Then select the data input radio.

Then select the column of Before for Group1 and column of After for Group 2.

Put zero for hypothesized difference select less than in the alternative.

Now click ok and the following result will be displayed in a new sheet.

Hypothesis Test: Paired Observations
	0.00000	hypothesized value
	21.69600	mean Before
	21.29500	mean After
	0.40100	mean difference (Before - After)
	0.44152	std. dev.
	0.13962	std. error
	10	n
	9	df
	2.87	t
	.9908	p-value (one-tailed, lower)

Conclusion:

The t-statistic for the test is 2.87 and the p-value is greater than the level of significance 0.05. So we have no evidence against the null hypothesis and we can conclude that there is no evidence to say that the body fat percentages of the students decreased by the end of the course.