(a) What sample size would be needed to estimate the true...

(a) What sample size would be needed to estimate the true proportion of American households that own more than one DVD player, with 90 percent confidence and an error of $\pm$ 0.02 ? (b) What sampling method would you recommend? Why?

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Key Concepts

Simple Random Sampling

A method of sampling where every member of the population has an equal probability of being selected. This technique minimizes selection bias and increases the likelihood that the sample is representative of the broader population, making it a recommended approach for estimating population proportions.

Sample Size Calculation

A process that uses the desired margin of error, confidence level, and an initial estimate of variability (often taken as 0.5 for proportions when no prior estimate is available) to determine the number of participants required in a study. The formula ensures that the sample is sufficiently large to achieve the desired precision in estimating the population parameter.

Margin of Error

This represents the maximum expected difference between the true population proportion and the observed sample proportion. It quantifies the range within which the true value is estimated to fall, given the confidence level.

Confidence Interval

A range of values derived from sample data that is likely to contain the true population parameter, given a specific confidence level. It reflects the uncertainty of the estimate and helps assess how close the sample proportion is to the true proportion.

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