Section 9.1

Estimating a Population Proportion

Learn how to construct confidence intervals for population proportions and determine necessary sample sizes.

1

Point Estimate

A point estimate is a single value used to estimate a population parameter. The sample proportion is the best point estimate for the population proportion .

x = number of successes (individuals with the characteristic)
n = sample size
2

Confidence Interval

A confidence interval is an interval of numbers based on a point estimate that is likely to contain the unknown parameter.

Model Requirements

Data are obtained randomly
Sample size is no more than 5% of population:

Interpretation: "We are 95% confident that the population proportion is between [lower] and [upper]." This means 95% of all possible samples will produce an interval that captures the true parameter.

Diagram showing that higher confidence levels produce wider intervals while lower confidence levels produce narrower intervals
3

Margin of Error

The margin of error (E) determines the width of the confidence interval.

The confidence interval is:

4

Determining Sample Size

With Prior Estimate

Use when a prior estimate from a previous study exists.

Without Prior Estimate

Use to ensure a large enough sample.

Important: Always round the resulting n up to the next integer.

5

Try It Yourself

Confidence Interval Calculator

Conditions Met

≥ 10 ✓

Calculations

:0.4200
:1.96
Margin of Error (E):0.0967
95.0% Confidence Interval
(0.3233, 0.5167)

Interpretation: We are 95.0% confident that the true population proportion is between 0.3233 and 0.5167.

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