Question

Let n₁=40 , p₁=0.60 and n₂=50 and p₂=0.40.

Given: H0:π1≤π2{"version":"1.1","math":"H_0: \pi_1 \leq \pi_2"}

Calculate the test statistic and p-value.

(a)-0.0261 and 0.4896 (b)1.8861 and 0.0296 (c) -0.9428 and 0.1729 (d) -0.4714 and 0.3939

Answer 1

Solution:

Given:

n₁=40 , p₁=0.60 and n₂=50 and p₂=0.40.

H0:π1≤π2 thus H1: H1:π1>π2

This is right tailed test.

Test statistic:

where

thus

P-value :

P-value = P( Z > z )

P-value = P( Z > 1.8861 )

P-value = 1 - P( Z < 1.8861 )

Use following excel command:

=1-NORM.S.DIST( z , cumulative)

=1-NORM.S.DIST(1.8861,TRUE)

=0.0296

Thus P-value = 0.0296

Thus correct answer is: (b)1.8861 and 0.0296