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Chapter 8: Q 57. (page 524)

Most people can roll their tongues, but many can’t. The ability to roll the tongue is

genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400students and find that 317can roll their tongues. The margin of error for a 95%confidence interval for the true proportion of tongue rollers among students is closest to which of the following?

a. 0.0008

b. 0.02

c. 0.03

d. 0.04

e. 0.05

Short Answer

Expert verified

Option (d) is correct.

Step by step solution

01

Given Information

It is given that (n)=400

(p^)=317400=0.7925

Confidence level=95%=0.95

02

Concept Used

Formula to be used is:

E=zα/2×p^×(1-p^)n

03

Calculating Margin of Error

Corresponding to 95%confidence level, zα2=1.96

Hence, margin of error,

E=za/2×p^×(1-p^)n

=1.96×(0.7925×(1-0.7925))400

=0.0397≈0.04

Option (d) is correct.

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Most popular questions from this chapter

More online sales Refer to Exercise 35. Calculate and interpret the standard error ofp^=xn for these data.

A quality control inspector will measure the salt content (in milligrams) in a random

sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content μ?

a. 90%confidence; n=25

b. 90%confidence; n=50

c. 95%confidence; n=25

d. 95%confidence; n=50

e. n = 100 at any confidence level

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: “The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.” You can safely conclude that

a. 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.

b. the percent of the population who jog is certain to be between 15% and 21%.

c. 95% of the population jog between 15% and 21% of the time.

d. we can be 95% confident that the sample proportion is captured by the confidence interval.

e. if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the true proportion p of all consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05or less at a 99%confidence level?

a. 550

b. 600

c. 650

d. 700

e. 750

Rating school food Latoya wants to estimate the proportion of the seniors

at her boarding school who like the cafeteria food. She interviews an SRS of 50of the 175 seniors and finds that 14 think the cafeteria food is good.
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