The National AIDS Behavioral Surveys interviewed a sample of adults in the cities where AIDS is most common. This sample included 782 heterosexuals who reported having more than one sexual partner in the past year. We can consider this an SRS of size 782 from the population of all heterosexuals in high-risk cities who have multiple partners. These people risk infection with the AIDS virus. Yet 292 of the respondents said they never use condoms. Is this strong evidence that more than one-third of this population never use condoms? (Use α = 0.05.)

Question

The National AIDS Behavioral Surveys interviewed a sample of adults in the cities where AIDS is most common. This sample included 782 heterosexuals who reported having more than one sexual partner in the past year. We can consider this an SRS of size 782 from the population of all heterosexuals in high-risk cities who have multiple partners. These people risk infection with the AIDS virus. Yet 292 of the respondents said they never use condoms. Is this strong evidence that more than one-third of this population never use condoms? (Use α = 0.05.)
Ho: p 	 
Ha: p 	 
z =

MathGuru · Answer

Try a proportional one-sample z-test for this one since this problem is using proportions.

Null hypothesis:
p ≤ .33
Alternate hypothesis:
p > .33

Using a formula for a proportional one-sample z-test with your data included, we have:
z = .37 - .33 -->test value minus population value
divided by
√[(.33)(.67)/782]-->.67 = 1 - .33; 782 = sample size

Finish the calculation. Use a z-table to determine the critical value for a one-tailed test at .05 level of significance. Determine whether or not to reject the null and conclude a difference (p > .33).

I hope this will help get you started.