Question number 11. When solving for the sample size required to estimate p to within a particular margin of error, under what circumstances do we use p̂ = .5? When the variance is equal to .5 or when we desire a most conservative sample size. When we have no prior information on the approximate value of p̂ or p. When the margin of error desired is less than or equal to .5 When the computed value of p̂ = .5 When p̂ = .4 and 1 - p̂ = .6 None of the above
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The question is about determining the sample size needed to estimate a population proportion (p) within a specified margin of error. The sample proportion (p̂) is often set to 0.5 in certain situations. Show more…
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In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: "If we have in mind a likely range for the observed value of p-hat, then, in light of Fig. 11.1, we should take as our educated guess for p-hat the value in the range closest to 0.5." Explain why.
Joanna Q.
If nothing is known about $p, .5$ can be substituted for $p$ in the sample-size formula for a population proportion. But when this is done, the resulting sample size may be larger than needed. Under what circumstances will using $p=.5$ in the sample-size formula yield a sample size larger than is needed to construct a confidence interval for $p$ with a specified bound and a specified confidence level?
In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: "If we have in mind a likely range for the observed value of $\hat{p},$ then, in light of Fig. 12.1 we should take as our educated guess for $\hat{p}$ the value in the range closest to 0.5" Explain why.
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