×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide

The article “HIV-positive Smokers Considering Quitting:

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 4E Chapter 5.2

Statistics for Engineers and Scientists | 4th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

4 5 1 372 Reviews
29
3
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

Chapter 5.2, Problem 4E is Solved
Step 4 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
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.

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

The article “HIV-positive Smokers Considering Quitting:

×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide
×
Reset your password