Question

A group of 100 college students and 100 college graduates was asked to reply to the question, "In general, do you enjoy reading a college textbook?" The following are the frequency counts for their responses on the 3-option item.

	Usually	Sometimes	Never
Students	30	25	45
Graduates	50	20	30

The critical value that you would use for an alpha level of .10 in the problem comparing college students' and graduates' enjoyment of reading textbooks is?

Answer 1

Solution:

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H₀: A frequency of reading a college textbook is independent of whether person is student or graduate.

Alternative hypothesis: H_a: A frequency of reading a college textbook is not independent of whether person is student or graduate.

We are given level of significance = α = 0.10

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 2

Number of columns = c = 3

Degrees of freedom = df = (r – 1)*(c – 1) = 1*2 = 2

α = 0.10

Critical value = 4.60517

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Row variable	Usually	Sometimes	Never	Total
Students	30	25	45	100
Graduates	50	20	30	100
Total	80	45	75	200

Expected Frequencies
	Column variable
Row variable	Usually	Sometimes	Never	Total
Students	40	22.5	37.5	100
Graduates	40	22.5	37.5	100
Total	80	45	75	200

(O - E)
-10	2.5	7.5
10	-2.5	-7.5

(O - E)^2/E
2.5	0.277778	1.5
2.5	0.277778	1.5

Chi square = ∑[(O – E)^2/E] = 8.555556

P-value = 0.013873

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that a frequency of reading a college textbook is not independent of whether person is student or graduate.