AP Statistics Confidence Intervals for a Proportion Worksheet (PDF)

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

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This confidence interval proportion worksheet 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.

These 20 problems practice AP Statistics topics 6.1 to 6.3. You will find critical values, check conditions, compute and interpret confidence intervals for a proportion, find margins of error and sample sizes, and use an interval to justify a claim.

AP Statistics · Common Core State Standards: AP STAT 6.1, AP STAT 6.2, AP STAT 6.3, HSS-IC.B.4

Confidence interval proportion worksheet: exercises 1 to 10

Exercise 1 – Critical values

Common critical values.

Find z* for a 90%, a 95%, and a 99% confidence interval. Explain why z* grows with the confidence level.

Exercise 2 – Check conditions

In a random sample of 80 of the 4,000 students at a school, 12 say they own an electric scooter. Check the conditions for a z interval for p.

Exercise 3 – Compute an interval

95% interval: (0.283, 0.437).

In a random sample of 150 teens, 54 say they use a social media app daily. Construct a 95% confidence interval for the proportion of all teens in the region who do.

Exercise 4 – Interpret the interval

Interpret the interval (0.283, 0.437) from the previous problem.

Exercise 5 – Interpret the confidence level

What does 95% confidence mean in the previous problem?

Exercise 6 – Identify errors

A student writes: “There is a 95% probability that the true proportion is between 0.283 and 0.437.” Explain the mistake.

Exercise 7 – 90 percent interval

In a random sample of 350 voters, 210 support a proposition. Find a 90% confidence interval for the proportion of all voters who support it.

Exercise 8 – 99 percent interval

Using the same data (210 of 350), find the 99% interval and compare its width with the 90% interval.

Exercise 9 – Margin of error

Poll result with margin of error 3.1 points.

A poll reports 48% support with a margin of error of 3.1 percentage points. Give the interval and interpret the margin of error.

Exercise 10 – Find p-hat and ME from an interval

Interval.

A 95% confidence interval for a proportion is (0.43, 0.57). Find the sample proportion and the margin of error.

Exercises 11 and up

Exercise 11 – Sample size

Sample size steps.

A club wants a 95% confidence interval with margin of error at most 0.04 for the proportion of members who support a new logo. No earlier estimate is available. Find the sample size.

Exercise 12 – Sample size with an estimate

A previous study suggests that about 30% of people recycle. How large a sample is needed for a 95% interval with margin of error at most 0.03?

Exercise 13 – Effect of n

Quadrupling n halves the margin of error.

A 95% interval based on n = 400 has margin of error 0.05. About what margin of error results from n = 1,600 at the same confidence?

Exercise 14 – Claim justification

95% interval: (0.283, 0.437).

A manager claims that exactly half of all teens use the app daily. Does the 95% interval (0.283, 0.437) support the claim?

Exercise 15 – Claim not rejected

A radio host claims that 50% of listeners like a song. In a random sample of 100 listeners, 46 like it. Use a 95% interval to evaluate the claim.

Exercise 16 – Large counts fails

A random sample of 40 people has 3 left-handed people. Explain why a z interval is not appropriate.

Exercise 17 – Wider or narrower?

For each change, say whether the margin of error gets larger or smaller: (a) larger sample size, (b) higher confidence level, (c) sample proportion closer to 0.5.

Exercise 18 – Convenience sample

A phone-in poll gets 900 responses, 63% in favor, and a 95% interval of (0.598, 0.662) is reported. Is the interval valid?

Exercise 19 – Multi-step

A random sample of 500 homes finds 185 with a smart thermostat. (a) Find a 95% interval. (b) Interpret. (c) Is it plausible that 40% of all homes have one?

Exercise 20 – Two sizes

Aisha computes 95% intervals for p from two samples with the same p-hat = 0.40: one has n = 100, the other n = 400. Compare the widths.

Key facts behind this confidence interval proportion worksheet

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 worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the confidence interval proportion worksheet as a PDF with the button below and keep it with your notes.

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