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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 α=0.05.

02

Explanation

To find that

zα/2=z0.05/2

=1.96

The confidence interval for pis form

p'-zα/2p'1-p'ntop'+zα/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±1.960(0.0153)

0.38±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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