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Chapter 8: Q. 50 (page 498)

50. Most people can roll their tongues, but many can鈥檛. 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 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to
(a) 0.008. (c) 0.03. (e) 0.208.
(b) 0.02. (d) 0.04

Short Answer

Expert verified

The correct answer is option (d)0.04.

Step by step solution

01

Given information

A simple random sample of 400 students and 317 can roll their tongues. To find the correct option for the margin of error for a 95%confidence interval for the true proportion of tongue rollers among students is closest.

02

Explanation

The sample proportion is calculated by dividing the number of successes by the sample size:
p^=xn

=317400

鈮�0.7925

Using table A, for confidence level 95%,

z伪/2=z0.025

=1.96

Determine the margin of error as follows:

E=z伪/2脳p^(1-p^)n

=1.96脳0.7925(1-0.7925)400

鈮�0.0397

鈮�0.04

As a result, the correct option is (d)0.04.

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Most popular questions from this chapter

High tuition costs Glenn wonders what proportion of the students at his school think that tuition is too high. He interviews an SRS of 50 of the 2400 students at his college. Thirty-eight of those interviewed think tuition is too high.

18. Explaining confidence The admissions director from Big City University found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen. Comment on whether or not each of the following explanations is correct.
(a) There is a 95%probability that the interval from 107.8to 116.2contains 渭.
(b) There is a 95%chance that the interval (107.8,116.2) contains x.
(c) This interval was constructed using a method that produces intervals that capture the true mean in 95% of all possible samples.
(d) 95%of all possible samples will contain the interval (107.8,116.2).

(e) The probability that the interval (107.8,116.2)captures 渭is either 0or 1, but we don鈥檛 know which.

56. The SAT again High school students who take the SAT Math exam a second time generally score higher than on their first try. Past data suggest that the score increase has a standard deviation of about 50 points.
How large a sample of high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence? Show your work.

NAEP scores Refer to Exercise 5. Below your sketch, choose one value of x inside the shaded region and draw its corresponding confidence interval. Do the same for one value of x outside the shaded region. What is the most important difference between these intervals?

In a poll,

I. Some people refused to answer questions.

II. People without telephones could not be in the sample.

III. Some people never answered the phone in several calls.

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(a) I only

(b) II only

(c) III only

(d) I, II, and III

(e) None of these

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