AP Statistics Significance Tests for a Proportion Worksheet (PDF)

AP Statistics math worksheet: Significance Tests for a Proportion – Maths PDF

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This test proportion worksheet for AP Statistics covers significance tests for a proportion (Common Core AP STAT 6.4, AP STAT 6.5, AP STAT 6.6, AP STAT 6.7, HSS-IC.A.2, HSS-IC.B.5), with a free PDF to print.

These 20 problems practice AP Statistics topics 6.4 to 6.7. You will write hypotheses, check conditions, compute z statistics and p-values, interpret p-values, reach conclusions, and describe Type I and Type II errors and power.

AP Statistics · Common Core State Standards: AP STAT 6.4, AP STAT 6.5, AP STAT 6.6, AP STAT 6.7, HSS-IC.A.2, HSS-IC.B.5

Test proportion worksheet: exercises 1 to 10

Exercise 1 – Write hypotheses

Write H0 and Ha and define p: (a) A company claims 90% of its packages arrive on time; a customer thinks the true rate is lower. (b) A coin is suspected of being unfair. (c) A teacher believes more than 60% of students support block scheduling.

Exercise 2 – Check conditions

A random sample of 120 of the 2,500 customers at a store is asked whether they prefer self-checkout; 54 say yes. Test H0: p = 0.40. Check the conditions.

Exercise 3 – Compute z

The four-step process for a test.

For the previous problem, compute the sample proportion, the standard error under H0, and the z statistic.

Exercise 4 – Find the p-value

P-value for z = 1.12.

With Ha: p > 0.40 and z = 1.12, find the p-value.

Exercise 5 – Conclude

Using alpha = 0.05 and the p-value 0.1314, state a conclusion in context.

Exercise 6 – Interpret a p-value

Two-sided p-value.

A test of H0: p = 0.5 gives a p-value of 0.021. Interpret the p-value in context if p is the true proportion of voters favoring a proposal and the sample is 400 voters.

Exercise 7 – Two-sided test

Two-sided p-value for z = 2.4.

A coin lands heads 62 times in 100 flips (suppose). Test H0: p = 0.5 against Ha: p not equal to 0.5.

Exercise 8 – Left-tailed test

Left-tailed p-value.

A factory says 95% of its bulbs last over 1,000 hours. In a random sample of 200 bulbs, 184 do. Test H0: p = 0.95 against Ha: p < 0.95.

Exercise 9 – Fail to reject

A test gives p-value 0.18 with alpha = 0.05. A student writes: “We accept H0, so p equals 0.5.” Correct the conclusion.

Exercise 10 – Alpha and the conclusion

The p-value is 0.03. State the conclusion for alpha = 0.05 and for alpha = 0.01.

Exercises 11 and up

Exercise 11 – Confidence interval and test

A 95% confidence interval for p is (0.52, 0.64). A two-sided test of H0: p = 0.50 at alpha = 0.05 is done. What is the conclusion?

Exercise 12 – Type I error

Type I and Type II errors.

A school tests H0: the new schedule does not change attendance, against Ha: it increases attendance. Describe a Type I error in context and its consequence.

Exercise 13 – Type II error

For the same test, describe a Type II error in context.

Exercise 14 – Probability of Type I

A test uses alpha = 0.10. What is the probability of a Type I error when H0 is true?

Exercise 15 – Increase power

Name two ways to increase the power of a one-proportion test and explain one of them.

Exercise 16 – Which error is worse?

A medical test screens for a serious disease. H0: the patient is healthy. Which error might be more serious, Type I or Type II? Explain.

Exercise 17 – Complete test

The four-step process for a test.

A random sample of 300 voters from a large city finds 132 who favor a transit tax. Test whether fewer than half of all voters in the city favor it, at alpha = 0.05.

Exercise 18 – Sample size effect

The same sample proportion 0.44 is observed in samples of n = 100 and n = 1,000 with H0: p = 0.5. Compare the z statistics and say what this shows.

Exercise 19 – Statistical vs practical

A very large study finds that 50.4% of births are boys, a statistically significant departure from 50% (p-value 0.004). Is the difference practically important?

Exercise 20 – Multi-step

In 400 random trials of a new treatment, 252 patients improved. The old treatment helped 60% of patients. Test whether the new treatment helps more than 60% at alpha = 0.01.

Key facts behind this test proportion worksheet

Key facts

H0 states no effect (p = p0); Ha is p > p0, p < p0, or p not equal to p0.
z = (p-hat – p0) / sqrt(p0(1 – p0)/n); check random, 10%, and large counts with p0.
p-value: probability of a result at least as extreme as observed, assuming H0 is true.
p-value < alpha: reject H0 (convincing evidence); otherwise fail to reject; never 'accept H0'.
Type I error: reject true H0 (probability alpha). Type II: fail to reject false H0; power = 1 – P(Type II).

How to use this test 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 test proportion worksheet as a PDF with the button below and keep it with your notes.

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