AP Statistics Confidence Intervals for a Proportion Test with Point Values (PDF)

AP Statistics math test: Confidence Intervals for a Proportion – Maths PDF

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This confidence interval proportion test for AP Statistics covers confidence intervals for a proportion (Common Core AP STAT 6.1, AP STAT 6.2, AP STAT 6.3, HSS-IC.B.4), with a free PDF to print.

This 45-minute test covers confidence intervals for a proportion, conditions, margin of error, sample size, and interpretation. Use the four-step process and write interpretations in context.

Time and points

About this test

Grade: AP Statistics
Chapter: Confidence Intervals for a Proportion
Standards: AP STAT 6.1, AP STAT 6.2, AP STAT 6.3, HSS-IC.B.4
Time: 45 minutes
Total: 20 points

Confidence interval proportion test: questions

Question 1 – Build an interval [4 pts]

In a random sample of 300 adults in a city, 135 say they own an electric vehicle charger or plan to buy one. (a) State and check the conditions. (2 points) (b) Construct a 95% confidence interval for the proportion of all adults in the city. (1 point) (c) Interpret the interval. (1 point)

Question 2 – Name the margin [1 pt]

Interval for the proportion.

An interval is (0.39, 0.51). What is the margin of error?

Question 3 – Interpret the level [2 pts]

Explain what it means that the interval in the previous question was made with 95% confidence.

Question 4 – Claim [2 pts]

A confidence interval.

A 95% confidence interval for a proportion is (0.38, 0.52). A company claims the true proportion is 0.55. Does the interval support the claim?

Question 5 – Sample size [3 pts]

How large a random sample is needed to estimate a proportion with a 99% confidence interval and margin of error at most 0.02, assuming no prior estimate? (3 points)

Question 6 – Conditions [2 pts]

A random sample of 50 students from a school of 800 has 4 who play the oboe. Can we use a z interval? Explain.

Question 7 – Effect of changes [3 pts]

Describe how each change affects the width of a confidence interval for a proportion: (a) increasing the confidence level from 90% to 99%; (b) increasing the sample size from 200 to 800; (c) a sample proportion changing from 0.50 to 0.10. (1 point each)

Question 8 – Process [3 pts]

Four steps.

List the four steps of the inference process and say what is done in the PLAN step for a one-proportion z interval. (3 points)

Key facts behind this confidence interval proportion test

Key facts

Interval: p-hat +/- z* sqrt(p-hat(1 – p-hat)/n); z* = 1.645, 1.960, 2.576 for 90%, 95%, 99%.
Conditions: Random, 10% (n < 10% of population), Large counts (n p-hat and n(1 - p-hat) at least 10).
Interpret the interval in context; interpret the level as the long-run capture rate.
Higher confidence or smaller n gives a wider interval; quadrupling n halves the margin of error.
A claimed value outside the interval is not plausible at that confidence level.

How to use this confidence interval proportion test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All AP Statistics chapters: AP Statistics math.

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