Question

In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago. In a sample of 50 women, 48 women said that they had less leisure time than they had 10 years ago. At α=0.10 is there a difference in the proportions?

Group of answer choices

A.P value=0.1404; fail to reject H₀

B.P value=0.1385; fail to reject H₀

C.P value=0.1193; fail to reject H₀

D.P value=0.1221; fail to reject H₀

Answer 1

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = Event

p₂: proportion where Sample 2 = Event

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Sample 1	50	44	0.880000
Sample 2	50	48	0.960000

Estimation for Difference

Difference	95% CI for Difference
-0.08	(-0.185183, 0.025183)

CI based on normal approximation

Test

Null hypothesis	H₀: p₁ - p₂ = 0
Alternative hypothesis	H₁: p₁ - p₂ ≠ 0

Method	Z-Value	P-Value
Normal approximation	-1.47	0.1404

The pooled estimate of the proportion (0.92) is used for the tests.
The normal approximation may be inaccurate for small samples.

Option:- .P value=0.1404; fail to reject H0