Question

A study of car accidents and drivers who use cell phones collects the following sample data.

	had accident in the last year	had no accidents in the last year
cellular phone user	23	282
non cellular phone user	46	407

1. Formulate the hypotheses
2. Determine the expected frequencies of those who had accidents in the last year to use for the chi-square test of independence.
3. Test the hypotheses

Please show your work. Thanks! and if possible can you explain how to do it in excel.

Answer 1

Solution:

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

Null hypothesis: H₀: The use of cellular phone and accident are independent of each other.

Alternative hypothesis: H_a: The use of cellular phone and accident are not independent of each other.

We assume 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 = 3.841459149

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Cellular phone use	Accident	Not Accident	Total
Yes	23	282	305
No	46	407	453
Total	69	689	758

Expected Frequencies
	Column variable
Cellular phone use	Accident	Not Accident	Total
Yes	27.76385224	277.2361478	305
No	41.23614776	411.7638522	453
Total	69	689	758

Calculations
(O - E)
-4.76385	4.763852
4.763852	-4.76385

(O - E)^2/E
0.817404	0.081859
0.550349	0.055115

Chi square = ∑[(O – E)^2/E] = 1.504727397

Test statistic = 1.504727397

P-value = 0.219945532

(By using Chi square table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the use of cellular phone and accident are independent of each other.