Question

A recent survey of 200 households showed that 8 had a single male as the head of the household. Forty years ago, a survey of 200 households showed that 6 had a single male as the head of the household. Can it be concluded that the proportion has changed, based on a 95% confidence interval? Recall the confidence interval is calculated as

Answer 1

H0: Null Hypothesis: P1 = P2 = 0

HA: Alternative Hypothesis: P1 - P2 0

n1 = 200

p1 = 8/200 = 0.04

n2 = 200

p2 = 6/200= 0.03

Q = 1 - P = 0.965

= 0.05

From Table critical values of Z = 1.96

Confidence interval:

(0.04 - 0.03) (1.96 X 0.0184)

= 0.01 0.0360

= ( - 0.0260 ,0.1460)

So,

Confidence interval:

- 0.0260 < P1 -P2 < 0.1460

Since 0 is included in the confidence interval, we cannot conclude that the proportion has changed.