Question

Independent random samples were selected from two binomial populations, with sample sizes and the number of successes given below.

	Population
	1	2
Sample Size	500	500
Number of Successes	121	149

Given:

H₀: (p₁ − p₂) = 0 versus H_a: (p₁ − p₂) ≠ 0

Solve:

Calculate the necessary test statistic. (Round your answer to two decimal places.)

z = ??

Calculate the p-value. (Round your answer to four decimal places.)

p-value = ??

Answer 1

p̂1 = 121 / 500 = 0.242
p̂2 = 149 / 500 = 0.298

Test Statistic :-
Z = ( p̂1 - p̂2 ) / √( p̂ * q̂ * (1/n1 + 1/n2) ))
p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 121 + 149 ) / ( 500 + 500 )
p̂ = 0.27
q̂ = 1 - p̂ = 0.73
Z = ( 0.242 - 0.298) / √( 0.27 * 0.73 * (1/500 + 1/500) )
Z = -1.99

P value = 2 * P ( Z < -1.99 ) = 0.0461 ( From Z table )