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All courses Math III · 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.
Your answer
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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

Identify the sample counts

\[\text{support}~\text{option}~A:~138,~\text{total}~\text{surveyed}:~200\]

These numbers let us compute the sample proportion of support.

02

Compute the sample proportion

\[\hat{p}~=~\frac{138}{200}~=~0.69\]

Divide the number of successes by the sample size.

03

Use the sample proportion as the estimate

\[\text{best}~\text{estimate}~\text{of}~\text{population}~\text{proportion}~=~0.69\]

In sampling, \(\hat{p}\) is used to estimate the true population proportion.

04

State the estimate clearly

\[\text{Sample}~\text{proportion}~0.69~\text{estimates}~\text{the}~\text{population}~\text{proportion}\]

That matches both the computed value and the question being asked.

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Another way

  1. You can also think of \(138/200\) as \(69/100\), which is \(0.69\) or \(69\%\).

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Common mistake

Using \(138\) alone as the estimate instead of turning it into a proportion out of the full sample of \(200\).