Unit 6 of AP Statistics delves into the crucial concepts of confidence intervals and hypothesis testing – skills essential for success on the AP exam. This practice test will help you solidify your understanding and identify areas needing further review. Remember, success in statistics relies not just on memorizing formulas, but on understanding the underlying logic and interpreting results in context.
Section 1: Confidence Intervals
Instructions: For each problem, clearly state the conditions, calculate the confidence interval, and interpret your findings in the context of the problem. Assume all necessary conditions are met unless otherwise stated.
Problem 1: A random sample of 50 students from a large university was surveyed about their average weekly spending on entertainment. The sample mean was $75 with a sample standard deviation of $20. Construct a 95% confidence interval for the average weekly entertainment spending of all students at the university.
Problem 2: A researcher wants to estimate the proportion of adults who support a new environmental policy. In a random sample of 1000 adults, 600 expressed support. Construct a 99% confidence interval for the population proportion.
Problem 3: Explain the relationship between sample size, confidence level, and the width of a confidence interval. How do these factors affect the precision of your estimate?
Section 2: Hypothesis Testing
Instructions: For each problem, state the hypotheses, calculate the test statistic, find the p-value, and state your conclusion in the context of the problem. Use a significance level of α = 0.05 unless otherwise specified.
Problem 4: A company claims that its new light bulb lasts an average of 1000 hours. A consumer advocacy group tests a random sample of 25 bulbs and finds a sample mean of 980 hours with a sample standard deviation of 50 hours. Test the company's claim at the 0.01 significance level.
Problem 5: A researcher wants to determine if there is a significant difference in the average height of men and women. A random sample of 50 men has a mean height of 70 inches with a standard deviation of 3 inches, while a random sample of 50 women has a mean height of 65 inches with a standard deviation of 2.5 inches. Conduct a two-sample t-test to test the hypothesis of no difference in average height.
Problem 6: Explain the difference between a Type I error and a Type II error in the context of hypothesis testing. What are the consequences of each type of error?
Section 3: Interpreting Results & Critical Thinking
Problem 7: A news article reports that a 95% confidence interval for the average income of a certain city is ($45,000, $55,000). Explain what this means in a way that someone without a statistics background could understand. What does it not mean?
Problem 8: Why is it important to check the conditions for inference before conducting a confidence interval or hypothesis test? What could happen if these conditions are violated?
Answer Key & Explanations (Available Separately)
This practice test provides a comprehensive review of key concepts within AP Statistics Unit 6. Remember to carefully consider the context of each problem and explain your reasoning thoroughly. A detailed answer key with explanations is available separately (contact your instructor or refer to your textbook for solutions). Good luck! Mastering these concepts will significantly boost your confidence and performance on the AP exam.
