Question

Consider the following competing hypotheses and accompanying sample data. (You may find it useful to reference the appropriate table: z table or t table)


H₀: p₁ − p₂ = 0.04
H_A: p₁ − p₂ ≠ 0.04

x1 = 154	x2 = 145
n1 = 253	n2 = 380

a. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Test Statistic ______

b. Find the p-value.

• 0.025  p-value < 0.05
• 0.05  p-value < 0.10
• p-value  0.10

• p-value < 0.01

• 0.01  p-value < 0.025

c. At the 1% significance level, what is the conclusion?

• Do not reject H₀; the difference between population proportions differs from 0.04.

• Reject H₀; the difference between population proportions does not differ from 0.04.

• Do not reject H₀; the difference between population proportions does not differ from 0.04.

• Reject H₀; the difference between population proportions differs from 0.04.

Answer 1

a)

	first population	2nd population
x=	154	145
n =	253	380
p̂=x/n=	0.6087	0.3816
estimated prop. diff =p̂1-p̂2    =		0.2271
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.4724
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0405
test stat z=(p̂1-p̂2)/Se =		4.62

b)

P value   =

0.0000

(from excel:2*normsdist(-4.62)

p-value < 0.01

c)since p value is less than 0.01

Reject H₀; the difference between population proportions differs from 0.04.