AP Statistics Significance Tests for a Proportion Test with Point Values (PDF)

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

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This test proportion test 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.

This 45-minute test covers hypotheses, one-proportion z tests, p-values, errors, and power. Follow the four-step process and write every conclusion in context.

Time and points

About this test

Grade: AP Statistics
Chapter: Significance Tests for a Proportion
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
Time: 45 minutes
Total: 20 points

Test proportion test: questions

Question 1 – One-proportion z test [5 pts]

A company says that at most 30% of its customers return products. A random sample of 200 of its many customers finds that 70 returned a product. Test whether the return rate is greater than 30% at alpha = 0.05. (State 1, Plan 1, Do 2, Conclude 1)

Question 2 – Interpret the p-value [2 pts]

In the previous test, interpret the p-value in context.

Question 3 – Errors [3 pts]

A farmer tests H0: a fertilizer has no effect on yield, against Ha: it increases yield. (a) Describe a Type I error in context. (1 point) (b) Describe a Type II error in context. (1 point) (c) What is the probability of a Type I error when alpha = 0.05? (1 point)

Question 4 – Two-sided p-value [2 pts]

Two-sided p-value.

For a two-sided test, z = 2.10. Find the p-value and state a conclusion at alpha = 0.05.

Question 5 – Conclusion language [2 pts]

A test yields a p-value of 0.27 (alpha = 0.05). Write a correct conclusion for a study of whether a new app increases the proportion of users who finish a lesson.

Question 6 – Alternative hypothesis [1 pt]

A tail.

A test statistic is z = 1.0 with a right tail shaded. Which alternative hypothesis matches the shading: p > p0, p < p0, or p not equal to p0?

Question 7 – Conditions [2 pts]

For H0: p = 0.02 and n = 150, check the large counts condition. Is a z test appropriate?

Question 8 – Decision [3 pts]

Decision rule.

A test of H0: p = 0.25 gives z = 1.40 for Ha: p > 0.25. (a) Find the p-value. (1 point) (b) State the decision at alpha = 0.10. (1 point) (c) State the decision at alpha = 0.05. (1 point)

Key facts behind this test proportion test

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 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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