Question

Independent random samples, each containing 80 observations, were selected from two populations. The samples from populations 1 and 2 produced 16 and 10 successes, respectively.
Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.1

(a) The test statistic is

(b) The P-value is

(c) The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that (p1−p2)=0
B. We can reject the null hypothesis that (p1−p2)=0 and accept that (p1−p2)≠0

Answer 1

The statistic software output for this problem is :

Two sample proportion summary hypothesis test:

p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ≠ 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	16	80	10	80	0.075	0.058329613	1.2857963	0.1985

(a) The test statistic is 1.286

(b) The P-value is 0.1985

(c) The final conclusion is :

A. There is not sufficient evidence to reject the null hypothesis that (p1−p2)=0