Quit smoking: In a survey of 444 HIV-positive smokers, 202 reported that they had used a nicotine patch to try to quit smoking. Can you conclude that less than half of HIV-positive smokers have used a nicotine patch

The p-value of the test is of 0.0287 < 0.05(standard significance level), which means that it can be concluded that less than half of HIV-positive smokers have used a nicotine patch.

Step-by-step explanation:

Test if less than half of HIV-positive smokers have used a nicotine patch:

At the null hypothesis, we test if the proportion is of at least half, that is:

At the alternative hypothesis, we test if the proportion is below 0.5, that is:

The test statistic is:

In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that

In a survey of 444 HIV-positive smokers, 202 reported that they had used a nicotine patch to try to quit smoking.

This means that

Value of the test statistic:

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.455, which is the p-value of z = -1.9.

Looking at the z-table, z = -1.9 has a p-value of 0.0287.

The p-value is of 0.0287 < 0.05(standard significance level), which means that it can be concluded that less than half of HIV-positive smokers have used a nicotine patch.

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