Question

A survey was taken asking what percent of gender takes public transportation and what percent drive. The results of the survey show that out of the 16 men survey 10 drive and 6 do not, where as with women 10 drive and 4 take public transportation.

Analyze the data by hand using the appropriate inferential technique and explain your choice

- Chi-Square

- Confidence Interval

  -  t-test,

- ANOVA

Answer 1

Solution:

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

Null hypothesis: H₀: Two categorical variables gender and whether they drive are independent.

Alternative hypothesis: H_a: Two categorical variables gender and whether they drive are dependent.

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 data as below:

Observed Frequencies
	Drive
Gender	Yes	No	Total
Men	10	6	16
Women	10	4	14
Total	20	10	30

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:

Expected Frequencies
	Drive
Gender	Yes	No	Total
Men	10.66667	5.333333	16
Women	9.333333	4.666667	14
Total	20	10	30

Calculations
(O - E)
-0.66667	0.666667
0.666667	-0.66667

(O - E)^2/E
0.041667	0.083333
0.047619	0.095238

Test Statistic = Chi square = ∑[(O – E)^2/E] = 0.267857

χ² statistic = 0.267857

P-value = 0.604773

(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 two categorical variables gender and whether they drive are independent.