A poll asked the following question: \"If the military draft were reinstated, wo

Question

A poll asked the following question: "If the military draft were reinstated, would you favor or oppose drafting women as well as men?" 44 percent of the 1000 people responding said that they would favor drafting women if the draft were reinstated. Using a 0.05 significance level, carry out a test to determine if there is convincing evidence that fewer than half of adult Americans would favor the drafting of women. (Round your test statistic to two decimal places and your P-value to four decimal places.) There is evidence to suggest that less than half of all adult Americans would favor the drafting of women. You may need to use the appropriate table in Appendix A to answer this question.

Explanation / Answer

Solution:

Here, we have to use one sample z test for the population proportion.

H0: p = 0.5 versus Ha: p < 0.5

This is a lower tailed or left tailed test.

We are given

n = 1000

p = 0.44, q = 1 – p = 1 – 0.44 = 0.56

= 0.05

Mean = np = 1000*0.44 = 440

SD = sqrt(pq/n) = sqrt(0.50*0.50/1000) = 0.015811

Z = (P – p) / sqrt(pq/n) = (0.44 – 0.50) / sqrt(0.50*0.50/1000) = -3.7947

Z = -3.7947

Lower critical value = -1.6449

P-value = 0.0001

There is sufficient evidence to suggest that less than half of all adult Americans would favour the drafting of women.

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