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1、*1 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 统计学精讲精练 主讲老师：黄逸昆 *2 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 2004 AP STATISTICS FREE-RESPONSE QUESTIONS(FORM B) STATISTICS SECTION Part A Questions 1-5 Spend about 65 minutes on this part of the exam. Percent of Section II grade75 *3 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 1 The Earths Moon
2、 has many impact craters that were created when the inner solar system was subjected to heavy bombardment of small celestial bodies. Scientists studied 11 impact craters on the Moon to determine whether there was any relationship between the age of the craters (based on radioactive dating of lunar r
3、ocks) and the impact rate (as deduced from the density of the craters). The data are displayed in the scatterplot below. *4 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 (a) Describe the nature of the relationship between impact rate and age. *5 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 Prior to fitting a linear regression model
4、, the researchers transformed both impact rate and age by using logarithms. The following computer output and residual plot were produced. *6 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 (b) Interpret the value of r 2. (c) Comment on the appropriateness of this linear regression for modeling the relationship betwee
5、n the transformed variables. *7 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 2 At a certain university, students who live in the dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food served there. The dining hall manager decided to do a survey to estima
6、te the proportion of students living in the dormitories who think that the quality of the food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question. *8 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 (a) In this setting, explain how bias ma
7、y have been introduced based on the way this convenience sample was selected and suggest how the sample could have been selected differently to avoid that bias. (b) In this setting, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been
8、worded differently to avoid that bias. *9 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 3Trains carry bauxite ore from a mine in Canada to an aluminum processing plant in northern New York state in hopper cars. Filling equipment is used to load ore into the hopper cars. When functioning properly, the actual weights
9、of ore loaded into each car by the filling equipment at the mine are approximately normally distributed with a mean of 70 tons and a standard deviation of 0.9 ton. If the mean is greater than 70 tons, the loading mechanism is overfilling. *10 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 (a) If the filling equipment
10、 is functioning properly, what is the probability that the weight of the ore in a randomly selected car will be 70.7 tons or more? Show your work. (b) Suppose that the weight of ore in a randomly selected car is 70.7 tons. Would that fact make you suspect that the loading mechanism is overfilling th
11、e cars? Justify your answer. (c) If the filling equipment is functioning properly, what is the probability that a random sample of 10 cars will have a mean ore weight of 70.7 tons or more? Show your work. (d) Based on your answer in part (c), if a random sample of 10 cars had a mean ore weight of 70
12、.7 tons, would you suspect that the loading mechanism was overfilling the cars? Justify your answer. *11 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 4. The principal at Crest Middle School, which enrolls only sixth-grade students and seventh-grade students, is interested in determining how much time students at th
13、at school spend on homework each night. The table below shows the mean and standard deviation of the amount of time spent on homework each night (in minutes) for a random sample of 20 sixth-grade students and a separate random sample of 20 seventh-grade students at this school. *12 单击此处编辑母版副 标题样式 单击
14、此处编辑母版标 题样式 Based on dotplots of these data, it is not unreasonable to assume that the distribution of times for each grade were approximately normally distributed. (a) Estimate the difference in mean times spent on homework for all sixth- and seventh-grade students in this school using an interval.
15、 Be sure to interpret your interval. *13 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 (b) An assistant principal reasoned that a much narrower confidence interval could be obtained if the students were paired based on their responses; for example, pairing the sixth-grade student and the seventh-grade student with t
16、he highest number of minutes spent on homework, the sixth-grade student and seventh-grade student with the next highest number of minutes spent on homework, and so on. Is the assistant principal correct in thinking that matching students in this way and then computing a matched- pairs confidence interval for the mean difference in time spent on homework is a better procedure than the one used in part (a) ? Explain why or why not. *14 单击此处编辑母版副 标题样式 单击此处编辑母版标 题样式 5. A researcher
