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Chapter 11: Q. 11.35 (page 460)

Obtain a sample size that will ensure a margin of error of at most the one specified.
Margin of error $= 0.03$
Confidence level $= 99 %$

Short Answer

Expert verified

The required sample size is $1842 .$

Step by step solution

01

Given information

The given data is

Margin of error $= 0.03$

Confidence level $= 99 %$

02

Explanation

Margin of error $= 0.03$

Confidence level $= 99 %$

When the margin of error is $0.03$ and the confidence level is $99 %$ , calculate the sample size.

With a $99 %$ confidence level, the required value of $z_{\frac{a}{2}}$ from table areas under the standard normal curve is $2.575 .$

The sample is

$n = 0.25 {(\frac{\frac{z_{\underline{α}}^{2}}{E}}{^{2}})}^{2}$

$= 0.25 {(\frac{2.575}{0.03})}^{2}$

$= 0.25 (7, 367.361)$

$= 1, 841.84$

$\approx 1842 .$

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Most popular questions from this chapter

Obtain a sample size that will ensure a margin of error of at most the one specified.

Margin of error $= 0.04$

Confidence level $= 99 %$

A Harris Roll asked Americans whether states should be allowed to conduct random drug tests on elected officials. Of $21, 355$ the respondents, $79 %$ said "yes."

a. Determine the margin of error for a $99 %$ confidence interval.

b. Without doing any calculations, indicate whether the margin of error is larger or smaller for a $90 %$ confidence interval. Explain your answer.

a. Determine the sample proportion.

b. Decide whether using the one-proportion $z -$ test is appropriate.

c. If appropriate, use the one-proportion $z -$ test to perform the specified hypothesis test.

$x = 8$

$n = 40$

$H_{0} : p = 0.3$

$H_{2} : p < 0.3$

$α = 0.10$

What does the margin of error for the estimate of a population proportion tell you?

Ballistic Fingerprinting. Guns make unique markings on bullets they fire and their shell casings. These markings are called holistic fingerprints. An ABCNEWS Podl examined the opinions of Americans on the enactment of a law "...that would require every gun sold in the United States to be test-fired first, so law enforcement would have its fingerprint in case it were ever used in a crime."

level, do the data provide sufficient evidence to conclude that women tend to favor ballistic fingerprinting more than men'?

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