Estimating Population Proportions and Sample Sizes

These flashcards cover essential concepts related to estimating population proportions and determining sample sizes, including definitions, formulas, and interpretations related to confidence intervals.

What is the population proportion?

The proportion (percentage) of the entire population that has the specified attribute.

What is the sample proportion?

The proportion (percentage) of a sample from the population that has the specified attribute.

What is a point estimate?

A single value used to estimate a population parameter.

What is the best point estimate of the population proportion?

The sample proportion, p.

Why do we use the sample proportion p as an estimator of p?

Because it is unbiased and the most consistent of the estimators.

What does a confidence interval represent?

An interval of values used to estimate the true value of a population parameter.

What is a confidence level?

The probability that the confidence interval contains the population parameter, such as 0.95 or 95%.

How is the confidence level related to alpha (α)?

The confidence level is 1 - α.

What does a critical value represent?

A number on the borderline separating sample statistics that are significantly high or low.

What is the formula for the margin of error (E)?

E = z(α/2) * √[(p̂ * q̂)/n] where p̂ is sample proportion, q̂ = 1 - p̂, and n is sample size.

How do you calculate a confidence interval for estimating a population proportion?

The formula is p - E < p < p + E.

What is the interpretation of a 95% confidence interval of 0.45 < p < 0.47?

We are 95% confident that the true population proportion p lies within this interval.

If the estimated sample size is not a whole number, what should you do?

Round the value of n up to the next larger whole number.

How many adults need to be surveyed to be 95% confident that the sample percentage is within three percentage points?

Use the formula for sample size estimation considering the desired margin of error.

What is StatCrunch?

A tool that can be used for statistical calculations, including confidence intervals for population proportion estimation.