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Chapter 10: Q. 3 (page 667)

Sports Illustrated planned to ask a random sample of Division I college athletes, "Do you believe performance enhancing drugs are a problem in college sports?" How many athletes must be interviewed to estimate the proportion concerned about the use of drugs within ±2%with 90%confidence?

(a)17(b)21(c)1680(d)1702(e)2401

Short Answer

Expert verified

The number of athletes interviewed is option (d) 1702

Step by step solution

01

Given Information

Given

ME=Margin of error=2%=0.02

c=confidence level=90%=0.90

02

Explanation

Formula sample size

p^known:n=zα/22p^q^ME2=zα/22p^(1-p^)ME2

p^unknown:n=zα/220.25ME2

For confidence level 1-α=0.90, determine zα/2=z0.05using the normal probability table in the appendix.

zα/2=1.65

A preliminary estimate p^is unknown, then the sample size is:

localid="1650382239919" n=zα/220.25ME2=1.652×0.250.022≈1702

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