ap stats unit 4 practice test

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03-02-2025

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Unit 4 of AP Statistics delves into the crucial world of inference for proportions – a cornerstone of statistical analysis. This practice test will help you solidify your understanding of confidence intervals and hypothesis tests for proportions, equipping you to confidently tackle the real exam. Remember, consistent practice is key to mastering these concepts!

Section 1: Multiple Choice

Instructions: Choose the best answer for each multiple-choice question.

1. A researcher wants to estimate the proportion of adults who support a new policy. A random sample of 1000 adults is selected, and 600 support the policy. What is the sample proportion?

   a) 0.30 b) 0.40 c) 0.60 d) 0.70

2. Which of the following conditions must be met to construct a confidence interval for a population proportion?

   a) The sample size must be large. b) The sample must be random. c) The population must be approximately normal. d) Both a) and b) e) Both b) and c)

3. A 95% confidence interval for a population proportion is (0.45, 0.55). Which of the following statements is true?

   a) There is a 95% chance that the population proportion is between 0.45 and 0.55. b) 95% of random samples from this population will produce a sample proportion between 0.45 and 0.55. c) If we took many random samples and constructed 95% confidence intervals, 95% of those intervals would contain the true population proportion. d) The margin of error is 0.10.

4. A researcher conducts a hypothesis test to determine if the proportion of people who prefer Brand A is greater than 0.5. The p-value is 0.03. At a significance level of α = 0.05, what is the conclusion?

   a) Fail to reject the null hypothesis. b) Reject the null hypothesis. c) There is not enough information to make a conclusion. d) Accept the null hypothesis.

5. What is the effect of increasing the sample size on the width of a confidence interval for a proportion?

   a) The width increases. b) The width decreases. c) The width remains the same. d) The effect cannot be determined.

Section 2: Free Response

Instructions: Show all your work for full credit.

1. A survey of 500 randomly selected college students found that 300 support a tuition increase.

   a) Construct a 90% confidence interval for the true proportion of college students who support the tuition increase. b) Interpret the confidence interval in context. c) If the survey had instead sampled 1000 students, how would this affect the width of the confidence interval? Explain your reasoning.

2. A company claims that at least 70% of its customers are satisfied. A random sample of 200 customers found that 130 were satisfied. Conduct a hypothesis test at a significance level of α = 0.01 to determine if there is enough evidence to reject the company's claim. Clearly state the null and alternative hypotheses, the test statistic, the p-value, and your conclusion.

Answer Key (Section 1)

1. c) 0.60
2. d) Both a) and b)
3. c) If we took many random samples and constructed 95% confidence intervals, 95% of those intervals would contain the true population proportion.
4. b) Reject the null hypothesis.
5. b) The width decreases.

This practice test provides a solid foundation for your AP Statistics Unit 4 exam preparation. Remember to review your notes, textbook, and other practice materials to further strengthen your understanding. Good luck!