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Chapter 11: Q. 11.34 (page 460)

Obtain a sample size that will ensure a margin of error of at most the one specified.
Margin of error $= 0.01$
Confidence level $= 90 %$

Short Answer

Expert verified

The required sample size is $6766 .$

Step by step solution

01

Given information

The given data is

Margin of error $= 0.01$

Confidence level $= 90 %$

02

Explanation

The given data is

Margin of error $= 0.01$

Confidence level $= 90 %$

When the margin of error is $0.01$ and the confidence level is $90 %$ , calculate the sample size.

With a $90 %$ confidence level, the required value of $z_{\frac{a}{2}}$ from table areas under the standard normal curve is $1.645$ .

Then the sample size is

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

$= 0.25 {(\frac{1.645}{0.01})}^{2}$

$= 0.25 (27, 060.25)$

$= 6, 765.06$

$\approx 6766 .$

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Most popular questions from this chapter

Margin of error $= 0.01$

Confidence level $= 95 %$

Educated guess $= 0.3$

(a) Obtain a sample size that will ensure a margin of error of at most the one specified (provided of course that the observed value of the sample proportion is further from $0.5$ that of the educated guess.

(b). Compare your answer to the corresponding one and explain the reason for the difference, if any.

$x_{1} = 30, n_{1} = 80, x_{2} = 15, n_{2} = 20; 95 %$ confidence interval

Obtain a sample size

Margin of error $= 0.01$

Confidence level $= 95 %$

likely range $= 0.2 - 0.4$

Fill in the blanks.

a. The mean of all possible sample proportions is equal to the

b. For large samples, the possible sample proportions have approximately a distribution.

c. A rule of thumb for using a normal distribution to approximate the distribution of all possible sample proportions is that both and are or greater.

The Organization for Economic Cooperation and Development (OECD) conducts studies on unemployment rates by country and publishes its findings in the document Main Economic Indicators. Independent random samples of $100$ and $75$ people in the civilian labor forces of Finland and Denmark, respectively, revealed $7$ and $3$ unemployed, respectively. Find a $95 %$ confidence interval for the difference between the unemployment rates in Finland and Denmark.

See all solutions

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