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Chapter 8: Q 33. (page 522)

The 10%condition When constructing a confidence interval for a population proportion, we check that the sample size is less than 10%of the population size.

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?

Short Answer

Expert verified

a. If sample size is less than 10%of population, observations are closer to independent.

b. The confidence interval will be inaccurate.

Step by step solution

01

Given Information

When constructing a confidence interval for a population proportion, it is checked that sample size is less than 10% of population size.

02

Necessity of this Condition

This condition is important due to the the fact that when sample size is less than 10%of population size, observations are closer to independent.

If this requirement is not met, it is not possible to calculate standard deviation of distribution.

03

If Population Size is not less than 10%

If this requirement is not met, it is not possible to calculate standard deviation of distribution correctly.

If standard deviation is not correct, confidence level will be inaccurate. There are less chances to obtain population parameter in confidence interval.

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Most popular questions from this chapter

Travel time to work A study of commuting times reports the travel times to work of a random sample of 20employed adults in New York State. The mean is x炉=31.25minutes and the standard deviation is sX=21.88

minutes. What is the standard error of the mean? Interpret this value in context.

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Price cuts (4.2) Stores advertise price reductions to attract customers. What type of price
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You have an SRS of 23observations from a large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98%confidence interval for the mean of the population?

a. 2.177

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c. 2.326

d. 2.500

e. 2.508
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