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Question

Based on a sample of 20 men, 40% owned cats

Based on a sample of 20 women, 55% owned cats

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Answer 1

Use difference of p's for null hypothesis that proportion who own cats are the same for men and women.

Assume a normal distribution for the proportional difference with mean 0 and a variance = p(1-p)(1/n₁+1/n₂)

The p for this case is the "pooled" p = (n₁p₁ + n₂p₂)/(n₁+n₂) =( p₁+p₂)/2 for this case (n₁=n₂)

So, use z statistic = (p₁-p₂)/sqrt((p(1-p)(2/n))

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