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Unformatted text preview: tatistic - parameter standard deviation of statistic Confidence interval: statistic (critical value ) (standard deviation of statistic)
Single-Sample Statistic Sample Mean Standard Deviation of Statistic σ n
p(1 − p) n Sample Proportion Two-Sample Statistic Difference of sample means Standard Deviation of Statistic
2 σ1 σ2 +2 n1 n2 Special case when σ 1 = σ 2 σ 1 1 + n1 n2 Difference of sample proportions p1 (1 − p1 ) p (1 − p2 ) +2 n1 n2 Special case when p1 = p2 p 1− p 16 1 1 + n1 n2
2 0observed − expected5 Chi-square test statistic = ∑
expected -5- 2002 AP® STATISTICS FREE-RESPONSE QUESTIONS
STATISTICS SECTION II Part A Questions 1-5
Spend about 65 minutes on this part of the exam. Percent of Section II grade—75 Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation. 1. In 1915 Einstein’s theory predicted that the curvature of space, denoted by γ , was 1, while Newtonian theory predicted it was 0. Since 1915 scientists have repeatedly found estimates of γ using various methods and procedures. Each estimate has a margin of error. The figure below displays (estimate ± margin of error) from each of 21 experiments. (a) Based on the display on page 6, describe how the precision of the estimates of γ has changed over time. (b) Write a few sentences describing the strength of evidence the experiments provide for the claim from Newtonian theory that g = 0. Your response must include justification based on the display. (c) Write a few sentences describing the strength of evidence the experiments provide for the claim from Einstein’s theory that g = 1. Your response must include justification based on the display. Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 6 GO ON TO THE NEXT PAGE. 2002 AP® STATISTICS FREE-RESPONSE QUESTIONS
2. A manufacturer of boots plans to conduct an experiment to compare a new method of waterproofing to the current method. The appearance of the boots is not changed by either method. The company recruits 100 volunteers in Seattle, where it rains frequently, to wear the boots as they normally would for 6 months. At the end of the 6 months, the boots will be returned to the company to be evaluated for water damage. (a) Describe a design for this experiment that uses the 100 volunteers. Include a few sentences on how it would be implemented. (b) Could your design be double blind? Explain. 3. There are 4 runners on the New High School team. The team is planning to participate in a race in which each runner runs a mile. The team time is the sum of the individual times for the 4 runners. Assume that the individual times of the 4 runners are all independent of each other. The individual times, in minutes, of the runners in similar races ar...
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