Question

Shortly after September 11th 2001, a researcher wanted to determine if the proportion of females that favored war with Iraq was significantly different from the proportion of males that favored war with Iraq. In a sample of 73 females, 28 favored war with Iraq. In a sample of 54 males, 29 favored war with Iraq.

a) Let p_F represent the proportion of females that favor the war, p_M represent the proportion of males that favor the war. What are the proper hypotheses?

H₀: p_F = p_M versus H_a: p_F > p_M H₀: p_F = p_M versus H_a: p_F < p_M     H₀: p_F < p_M versus H_a: p_F = p_M H₀: p_F = p_M versus H_a: p_F ≠ p_M

b) What is the test statistic? Compute the statistic using male statistics subtracted from female statistics. Give your answer to four decimal places.

c) What is the P-value for the test? Give your answer to four decimal places.
d) Using a 0.01 level of significance, what conclusion should be reached?

The proportion of females that favor the war and the proportion of males that favor the war are significantly different because the P-value is greater than 0.01. The proportion of females that favor the war and the proportion of males that favor the war are not significantly different because the P-value is greater than 0.01.      The proportion of females that favor the war and the proportion of males that favor the war are not significantly different because the P-value is less than 0.01. The proportion of females that favor the war and the proportion of males that favor the war are significantly different because the P-value is less than 0.01.

e) What is the lower endpoint of a 99% confidence interval for the difference between the proportion of females that favor the war and the proportion of males that favor the war? Give your answer to four decimal places.

f) What is the upper endpoint of a 99% confidence interval for the difference between the proportion of females that favor the war and the proportion of males that favor the war? Give your answer to four decimal places

Answer 1

a)

p_F = p_M versus H_a: p_F ≠ p_M

_b)

	male		female
x1                =	29	x2                =	28
p̂1=x1/n1 =	0.5370	p̂2=x2/n2 =	0.3836
n1                       =	54	n2                       =	73
estimated prop. diff =p̂1-p̂2    =		0.1535
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.4488
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0893
test stat z=(p̂1-p̂2)/Se =		1.7191

c)

from excel: P value   =2(1-normsdist(1.7191))=

0.0856

d)The proportion of females that favor the war and the proportion of males that favor the war are not significantly different because the P-value is greater than 0.01.

e)

std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0886
for 99 % CI value of z=		2.576
margin of error E=z*std error =		0.2281
lower bound=(p̂1-p̂2)-E=		-0.0746

f)

Upper bound=(p̂1-p̂2)+E=

0.3816