This comprehensive practice test covers the key concepts in AP Statistics Unit 5: Inference for Proportions. It's designed to help you solidify your understanding and prepare for the AP exam. Remember to show your work and justify your answers! Good luck!
Section 1: Multiple Choice
Instructions: Choose the best answer for each multiple-choice question.
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Which of the following conditions must be met to perform a one-sample z-test for a population proportion? a) The sample size must be large enough such that both np ≥ 10 and n(1-p) ≥ 10. b) The sample must be a simple random sample. c) The population must be approximately normal. d) Both a and b. e) a, b, and c.
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A researcher wants to test whether the proportion of adults who support a new policy is greater than 0.6. They collect a random sample of 100 adults and find that 65 support the policy. What is the test statistic for this hypothesis test? (Round to two decimal places)
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What does a p-value represent in the context of a hypothesis test for a proportion? a) The probability that the null hypothesis is true. b) The probability of observing the sample data (or more extreme data) if the null hypothesis is true. c) The probability that the alternative hypothesis is true. d) The probability of making a Type I error.
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A 95% confidence interval for a population proportion is calculated to be (0.45, 0.55). Which of the following statements is TRUE? a) There is a 95% probability that the population proportion is between 0.45 and 0.55. b) 95% of the sample proportions will fall within this interval. c) If we were to repeat the sampling process many times, 95% of the resulting confidence intervals would contain the true population proportion. d) The margin of error is 0.10.
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How does increasing the sample size affect the width of a confidence interval for a population proportion? a) It increases the width. b) It decreases the width. c) It has no effect. d) It depends on the population proportion.
Section 2: Free Response
Instructions: Answer the following free-response questions completely and show all your work.
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A company claims that 80% of its customers are satisfied with its product. A consumer advocacy group wants to test this claim. They randomly sample 200 customers and find that 140 are satisfied. Conduct a hypothesis test at the α = 0.05 significance level to determine whether the company's claim is accurate. Clearly state your hypotheses, test statistic, p-value, and conclusion in context.
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A researcher wants to estimate the proportion of students who prefer online classes to in-person classes. They want to construct a 99% confidence interval with a margin of error of no more than 0.03. What is the minimum sample size needed if they assume that the proportion is around 0.5?
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Explain the difference between a Type I error and a Type II error in the context of hypothesis testing for a proportion. What are the consequences of each type of error?
Answer Key (Section 1: Multiple Choice)
- d)
- (Requires Calculation - Should be around 1.5)
- b)
- c)
- b)
This practice test provides a solid foundation for your AP Statistics Unit 5 review. Remember to consult your textbook and class notes for further clarification on any concepts you find challenging. Good luck with your studies!
