Practice Proportional Data in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Proportional data expresses quantities as fractions or percentages of a whole, enabling fair comparison across groups of different sizes.

Raw counts can mislead when groups differ in size — saying "100 people in City A vs. 100 in City B have a disease" ignores that City A may be ten times larger.

Example 1

easy
In a survey, 45 out of 180 students prefer online learning. Calculate the sample proportion \hat{p} and interpret it.

Example 2

medium
A poll finds \hat{p} = 0.52 supporting a candidate from n=400 voters. Calculate the standard error of \hat{p} and construct an approximate 95% confidence interval.

Example 3

easy
In a class of 25 students, 15 passed the test. Calculate \hat{p} and find the number expected to pass in a class of 100 using this estimate.

Example 4

hard
Compare two proportions: Group A: 30/120 support policy. Group B: 45/150 support policy. Test if the proportions differ using a z-test for difference in proportions.
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