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# The article “HIV-positive Smokers Considering Quitting: ISBN: 9780073401331 38

## Solution for problem 4E Chapter 5.2

Statistics for Engineers and Scientists | 4th Edition

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Problem 4E

The article “HIV-positive Smokers Considering Quitting: Differences by Race/Ethnicity” (E. Lloyd- Richardson, C. Stanton, et al., Am J Health Behav, 2008:3-15) surveyed 444 HIV-positive smokers. Of these, 170 reported that they had used a nicotine patch. Consider this to be a simple random sample.

a. Find a 95% confidence interval for the proportion of HIV-positive smokers who have used a nicotine patch.

b. Find a 99% confidence interval for the proportion of HIV-positive smokers who have used a nicotine patch.

c. Someone claims that the proportion is less than 0.40. With what level of confidence can this statement be made?

d. Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.03.

e. Find the sample size needed for a 99% confidence interval to specify the proportion to within ±0.03.

Step-by-Step Solution:

Step 1 of 4:

An article says that 444 people survived from HIV. Of these,170 reported that they had used a nicotine patch.

We have to find

95% CI for the proportion of HIV-positive smokers who have used a nicotine patch. 99% CI for the proportion of HIV- positive smokers who have used a nicotine patch.With what level of confidence the the claim that the proportion is less than 0.40 made. Find the sample size needed for 95% CI to specifies the proportion within .Find the sample size needed for 99% CI to specifies the proportion within .

Step 2 of 4 :

95% CI for the proportion of HIV- positive smokers who have used nicotine patch.

Let X be the number of success in an independent bernoulli trials with success probability P, so that X~B(n,P).

Lets define = n+4.

And = Then a level 100(1- confidence interval for P is Let X denote the number of people who had used nicotine. And n be the total number of HIV-positive smokers. X   =  170

n    =  444  444+4

=  448

And =  0.3839.

Since here the Z-score is = We can find from the standard normal table, So the 95% confidence interval for the proportion of HIV-positive smokers they have used nicotine.

( 0.3839  ) (  0.3388  , 0.4289 )

Therefore the 95% confidence interval for the proportion of HIV-positive smokers they had used nicotine  (0.3388, 0.4289).

(b) The 99% CI for the proportion of HIV- positive smokers they had used nicotine.

Since the Z- score is = We can find the value from the standard normal table, .

So the 99% CI for the proportion of HIV-positive smokers they had used nicotine.

( 0.3839  ) (  0.3246  , 0.4431)

Therefore the 99% CI for the proportion of  HIV- positive smokers they had used nicotine (0.3246, 0.4431).

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

The answer to “The article “HIV-positive Smokers Considering Quitting: Differences by Race/Ethnicity” (E. Lloyd- Richardson, C. Stanton, et al., Am J Health Behav, 2008:3-15) surveyed 444 HIV-positive smokers. Of these, 170 reported that they had used a nicotine patch. Consider this to be a simple random sample.a. Find a 95% confidence interval for the proportion of HIV-positive smokers who have used a nicotine patch.________________b. Find a 99% confidence interval for the proportion of HIV-positive smokers who have used a nicotine patch.________________c. Someone claims that the proportion is less than 0.40. With what level of confidence can this statement be made?________________d. Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.03.________________e. Find the sample size needed for a 99% confidence interval to specify the proportion to within ±0.03.” is broken down into a number of easy to follow steps, and 131 words. This full solution covers the following key subjects: proportion, confidence, Positive, Find, smokers. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 4E from chapter: 5.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 4E from 5.2 chapter was answered, more than 508 students have viewed the full step-by-step answer.

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