Question

	Registered Course
	Online	Campus
<$40,000	35	56
			$40,000 - $75,000	24	41
>$75,000	19	26

The data listed above is from a study conducted to determine whether students of certain income brackets preferred online or face-to-face courses.

a.) Why must we use a non-parametric test for such data?

b.) Conduct a chi-square test for independence on the data set, and interpret your results.

Answer 1

(a) Because we have 2 categorical variables with unknown sample parametric.

(b) The hypothesis being tested is:

H0: Students of certain income brackets preferred online or face-to-face courses

Ha: Students of certain income brackets did not preferred online or face-to-face courses

		Col 1	Col 2	Total
Row 1	Observed	35	56	91
	Expected	35.31	55.69	91.00
	O - E	-0.31	0.31	0.00
	(O - E)² / E	0.00	0.00	0.00
Row 2	Observed	24	41	65
	Expected	25.22	39.78	65.00
	O - E	-1.22	1.22	0.00
	(O - E)² / E	0.06	0.04	0.10
Row 3	Observed	19	26	45
	Expected	17.46	27.54	45.00
	O - E	1.54	-1.54	0.00
	(O - E)² / E	0.14	0.09	0.22
Total	Observed	78	123	201
	Expected	78.00	123.00	201.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	0.20	0.13	0.32
		.32	chi-square
		2	df
		.8510	p-value

The p-value is 0.8510.

Since the p-value (0.8510) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that students of certain income brackets preferred online or face-to-face courses.