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Chapter 8: Q. 50 (page 498)

50. 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 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

≈0.7925

Using table A, for confidence level 95%,

zα/2=z0.025

=1.96

Determine the margin of error as follows:

E=zα/2×p^(1-p^)n

=1.96×0.7925(1-0.7925)400

≈0.0397

≈0.04

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

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