Question

The different types of vehicles that women versus men drive daily will be compared. We are going to be comparing the proportion of women that drive a car versus men that drive a car as their main source of transportation. The survey was done for 200 women and 200 men. Out of the 200 women 130 drove a car as their main source of transportation and out of 200 men 108 drove a car as their main source of transportation. I believe that theproportion of women car drivers is greater than the proportion of men car drivers. We will assume that this sample was an independent simple ransom sample of women to men that drove a car as their main source of transportation.

Test this Hypothesis at .08 significance level where p1 = proportion of women and p2 = proportion of men

Answer 1

Solution:

Here, we have to use z test for the difference between two population proportions.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: The proportion of women car drivers is same as the proportion of men car drivers.

Alternative hypothesis: H_a: The proportion of women car drivers is greater than the proportion of men car drivers.

H₀: p₁ = p₂ versus H_a: p₁ > p₂

Where, p1 = proportion of women and p2 = proportion of men

We are given level of significance = α = 0.08

The test statistic formula is given as below:

Z = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Where,

X1 = 130

X2 = 108

N1 = 200

N2 = 200

P = (X1+X2)/(N1+N2) = (130 + 108) / (200 + 200) = 0.5950

P1 = X1/N1 = 130/200 = 0.65

P2 = X2/N2 = 108/200 = 0.54

Z = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Z = (0.65 – 0.54) / sqrt(0.5950*(1 – 0.5950)*((1/200) + (1/200)))

Z = (0.11) / sqrt(0.5950*(1 – 0.5950)*((1/200) + (1/200)))

Z = 2.2408

P-value = 0.0125

(by using z-table)

P-value < α = 0.08

So, we reject the null hypothesis

There is sufficient evidence to conclude that the proportion of women car drivers is greater than the proportion of men car drivers.