Question

A sample of 500 respondents in a metropolitan area was selected to determine certain information regarding consumer behavior.
Among the questions was: Do you enjoy shopping for clothing? To which, of 240 men, 136 answered yes and, of 260 women, 224 also responded affirmatively.
Is there evidence of a significant difference between the proportion of men and women who enjoy buying clothes at a level of 1%?

Answer 1

Solution:

Here, we have to use z test for difference in population proportions.

H₀: p₁ = p₂ versus H_a: p₁ ≠ p₂

Test statistic is given as below:

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

Where,

N1 = 240

N2 = 260

X1 = 136

X2 = 224

P1 = X1/N1 = 136/240 = 0.566666667

P2 = X2/N2 = 224/260 = 0.861538462

α = 0.01

P = (X1 + X2) / (N1 + N2) = (136+224)/(240+260) = 0.72

Z = (0.566666667 – 0.861538462)/sqrt(0.72*(1 - 0.72)*((1/240)+(1/260)))

Z = -7.3366

P-value = 0.0000

(by using z-table)

P-value < α = 0.01

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is significant difference between the proportion of men and women who enjoy buying clothes at a level of 1%.