Sample Hypothesis Proportion

Question

You are testing the claim that the proportion of men who own cats is smaller than the proportion of women who own cats.

You sample 200 men, and 65% own cats.

You sample 80 women, and 50% own cats.

Find the test statistic, rounded to two decimal places.

Answer 1

For two population proportion, the formula that we need to use is z test statistic:

z₀ = _{____}p_{1 -} p_{2____} where p = x₁ + x₂

√[p (1-p)(1/n₁ + 1/n₂). n₁ + n₂

For population of men:

n₁ = 200, p₁ = 0.65, x₁ = 65% of 200 = 130

For population of women:

n₂ = 80, p₂ = 0.5, x₂ = 50% of 80 = 40

p = (130+40) / (200+80) =170/280 = 0.607...

Substitute (Don't round off the p yet in your calculator until you reach the final answer) :

z₀ = ___p_{1 -} p_{2_______} = ___________0.65 - 0.5___________

√[p (1-p)(1/n₁ + 1/n₂)] √[(0.607...) (1-0.607...)(1/200 + 1/80)]

z₀ ≈ 2.32