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Chapter 8: Q.6 (page 523)

Do you go to church? The Gallup Poll plans to ask a random sample of adults whether they attended a religious service in the last 7days. How large a sample would be required to obtain a margin of error of 0.01ina99%confidence interval for the population proportion who would say that they attended a religious service? Show your work.

- Construct and interpret a confidence interval for a population proportion.

- Explain how practical issues like nonresponse, under coverage, and response bias can affect the interpretation of a confidence interval.

Short Answer

Expert verified

The sample size is 1657716577

Step by step solution

01

Step-1 Given Information

Given in the question that,

Margin of errorE=1%=0.01

Confidence level=99%we have to find How large a sample would be required to obtain a margin of error and confidence interval for the population proportion who would say that they attended a religious service.

02

Step-2 Explanation

The formula to compute the sample size is:

n=p⏞1-p^zE2

Calculation:

From the standard normal table, the z-score at 99%confidence level is 2.576.

Consider, sample proportion to be 0.05.

The sample size is calculated as:

n=p^1-p^zE2

=0.501-0.502.5760.012=0.501-0.502.5760.012

=16577

Thus, the sample size is 16577.

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Most popular questions from this chapter

How confident? The figure below shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for each sample. Which confidence level—80%,90%,95%, or 99%— do you think was used? Explain

Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology.

(a) A 98% confidence interval based on n=22observations.

(b) A 90%confidence interval from an SRS of 10observations.

(c) A 95% confidence interval from a sample of size7.

Velvetleaf is a particularly annoying weed in cornfields. It produces lots of seeds, and the seeds wait in the soil for years until conditions are right for sprouting. How many seeds do velvetleaf plants produce? The Fathom histogram below shows the counts from 28plants that came up in a cornfield when no herbicide was used. Explain why it would not be wise to use a one-sample tinterval to estimate the mean number of seeds μproduced by velvetleaf plants.

How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4inches long and 1.5inches square? A random sample of 20similar pieces of Douglas fir from a large batch was selected for a science class. The Fathom boxplot below shows the class’s data. Explain why it would not be wise to use a one-sample t interval to estimate the population meanμ.

You have an SRS of 23 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean M of the population if S is unknown?

(a) 2.508

(b) 2.500

(c) 2.326

(d) 2.183

(e) 2.177
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