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Chapter 11: Q.11.52 (page 460)

Drinking Habits. In a nationwide survey, conducted by Pulse Opinion Research, LLC for Rasmussen Reports, 1000 American adults were asked, among other things, whether they drink alcoholic beverages at least once a week; 38% said "yes." Determine and interpret a 95% confidence interval for the proportion, p, of all American adults who drink alcoholic beverages at least once a week.

Short Answer

Expert verified

The confidence interval for the proportion of all-American adults who drink alcoholic beverages at least once a week is 0.350 to 0.410, according to the 95% confidence interval.

Step by step solution

01

Given Information

When xand n-xare both 5the one-proportion z-interval technique is appropriate if the number of proportions is larger than one.

It has a 95%confidence interval, which means that 伪=0.05.

02

Explanation

To find that

z伪/2=z0.05/2

=1.96

The confidence interval for pis form

p'-z伪/2p'1-p'ntop'+z伪/2p'1-p'ni.e.0.38-1.9600.38(1-0.38)1000to0.38-1.9600.38(1-0.38)1000i.e.0.38卤1.960(0.0153)

0.38卤0.0299

(0.350,0.410)

The 95%confidence interval for the percentage of all adult Americans who drink alcoholic beverages at least once a week is (0.350,0.410).

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Most popular questions from this chapter

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A poll conducted by Gallup in December 2013asked a sample of American adults whether they approved of the way President Obama was doing his job; 42%said yes, with a margin of error of plus or minus 3percentage points. During that same time period, Quinnipiac University asked the same question of a sample of American adults; 38%said yes, with a margin of error of plus or minus2 percentage points. Can the conclusions of both polls be correct? Explain your answer.

We have given a likely range for the observed value of a sample proportionp^

0.2orless

a. Based on the given range, identify the educated guess that should be used for the observed value of p^to calculate the required sample size for a prescribed confidence level and margin of error.

b. Identify the observed values of the sample proportion that will yield a larger margin of error than the one specified if the educated guess is used for the sample-size computation.

In this Exercise, we have given the number of successes and the sample size for a simple random sample from a population. In each case,

a. use the one-proportion plus-four z-interval procedure to find the required confidence interval.

b. compare your result with the corresponding confidence interval found in Exercise 11.25-11.30, if finding such a confidence interval was appropriate.

role="math" localid="1651326935007" x=10,n=40,90%level

x1=18,n1=30,x2=10,n2=20;95%confidence interval
See all solutions

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