Shortly after September 11th 2001, a researcher wanted to determine if the propo

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 74 females, 30 favored war with Iraq. In a sample of 52 males, 34 favored war with Iraq.

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

A. H0: pF = pM versus Ha: pF < pM

B. H0: pF = pM versus Ha: pF > pM

C. H0: pF < pM versus Ha: pF = pM

D. H0: pF = pM versus Ha: pF pM

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?

A. 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.

B. 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.

C. 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.

D. 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.

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.

Explanation / Answer

The statistical 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
HA : p1 - p2 0

Hypothesis test results:

99% confidence interval results:

Hence,

a) Hypotheses:

H0: pF = pM versus Ha: pF pM

Option D is correct.

b) Test statistic = -2.7462

c) p - Value = 0.0060

d) 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.

Option A is correct.

e) lower endpoint = -0.4731

f) Upper endpoint = -0.0237

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