One-Proportion Confidence Intervals, Plus-Four Adjustment, and Sample Size Planning

All flashcards

What is a population proportion?

The fraction of a population with a specified characteristic, commonly represented by $p$.

How is the sample proportion calculated?

Divide the observed number of successes by the sample size: $p'=x/n$.

How are the estimated success and failure proportions related?

They sum to 1: $q'=1-p'$.

What is the error bound for a proportion?

The margin of error is $EBP=z_{\alpha/2}\sqrt{p'q'/n}$.

How does the plus-four adjustment change the data used in an interval?

It adds two successes and two failures before calculating the adjusted interval.

Quiz questions

1. A 95% confidence interval for a population proportion is calculated from a random sample. What does the 95% confidence level describe?Answer: About 95% of intervals from repeated samples would contain the true proportion.
2. Which kind of data is suited to a one-proportion interval?Answer: A count of outcomes classified into two categories.
3. Under the stated recommendation, when should the plus-four method be considered?Answer: When confidence is at least 90% and the original sample has at least 10 observations.
4. If all other inputs are held fixed, what happens to the required sample size when the confidence level increases?Answer: It increases because the critical $z$ value becomes larger.
5. When no prior estimate of a population proportion is available, why use $p'=0.50$ and $q'=0.50$ for sample-size planning?Answer: Their product gives a conservative, generally largest sample-size requirement.