Question

We interviewed two groups of 50 college students respectively from UIC and DePaul to know if they rather watch NFL Football vs. some other sport on Sunday.

Actual Data

	UIC	DePaul	Row Total
Football	15	25	40
Other Sport	35	25	60
Total	50	50	100

Based on the statistics above, we need to determine if there is a relationship between the university of a student and watching Football. Answer to the following questions to arrive at the conclusion.

• What are Ho and Ha?
• What are the chi-square values?
• What is the degrees of freedom?
• What is the p-value?
• For alpha=0.05, what would be our statistical conclusion?
• Write out the full conclusion in English

Please show work

Answer 1

Solution:

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

Null hypothesis: H0: There is no relationship between the University of a Student and watching Football.

Alternative hypothesis: Ha: There is a relationship between the university of a student and watching Football.

We assume/given level of significance = α = 0.05

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 = 2

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

α = 0.05

Critical value = 3.841459

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Row variable	UIC	DePaul	Total
Football	15	25	40
Other Sport	35	25	60
Total	50	50	100

Expected Frequencies
	Column variable
Row variable	UIC	DePaul	Total
Football	20	20	40
Other Sport	30	30	60
Total	50	50	100

Calculations
(O - E)
-5	5
5	-5

(O - E)^2/E
1.25	1.25
0.833333	0.833333

Test Statistic = Chi square = ∑[(O – E)^2/E] = 4.166667

χ2 statistic = 4.166667

P-value = 0.041227

(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 there is a relationship between the University of a Student and watching Football.