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All courses Algebra II · S-IC.4 50 of 55
Use sample data to estimate population means/proportions and develop margins of error using simulation.

Use a sample proportion to estimate a population proportion

Problem
Of \(200\) surveyed people, \(138\) support proposal A. Compute the sample proportion and use it to estimate the population proportion.
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Hint

Compute the sample proportion by dividing the number who support option A by the sample size.

The best estimate of a population proportion is the sample proportion \(\hat{p}\).

Solution walkthrough

01

Write the sample-proportion formula

\[\text{sample}~\text{proportion}=\text{number}~\text{supporting}~A/\text{number}~\text{surveyed}\]

A proportion compares the favorable count with the total sample size.

02

Substitute the observed counts

\[\text{sample}~\text{proportion}=138/200\]

The prompt supplies 138 supporters among 200 surveyed people.

03

Compute the decimal

\[138/200=0.69\]

Dividing the observed support count by the sample total gives sixty-nine hundredths.

04

Interpret the point estimate

\[138/200~=~0.69~\text{estimates}~\text{the}~\text{population}~\text{proportion}.\]

The sample proportion is used as a point estimate, not as a guaranteed population value.

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Another way

  1. Convert 138 out of 200 to a percent: multiplying 0.69 by 100 gives 69%, the same point estimate.

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Common mistake

Do not use the count 138 alone as a proportion; the total sample size 200 must be the denominator.

Solution walkthrough video