The National AIDS Behavioral Surveys interviewed a sample of

The National AIDS Behavioral Surveys interviewed a sample of adults in the cities where AIDS is most common. This sample included 795 heterosexuals who reported having more than one sexual partner in the past year. We can consider this an SRS of size 795 from the population of all heterosexuals in high-risk cities who have multiple partners. These people risk infection with the AIDS virus. Yet 320 of the respondents said they never use condoms. Is this strong evidence that more than one-third of this population never use condoms? (Use ? = 0.05.)

P-value

P > 0.1000.050 < P < 0.100    0.025 < P < 0.0500.010 < P < 0.0250.001 < P < 0.010P < 0.001

Conclusion:

There is evidence that more than one-third of this group never use condoms.

There is no evidence that more than one-third of this group never use condoms.   

Solution

H_o: p=1/3

H_a: p >1/3

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z = (phat-p)/sqrt(p*(1-p)/n)

=(320/795 -1/3)/sqrt((1/3)*(2/3)/795)

=4.14

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It is a right-tailed test.

So the p-value= P(Z>4.14) = 0.000017 (from standard normal table)

P < 0.001

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There is evidence that more than one-third of this group never use condoms.