課程名稱：統計學 課程性質：必修 課程範圍：第1~4章 (introduction ~ probability) 開課教師：鄭宗記 開課學院：商學院 開課系級：統計系 考試日期(年月日)：2011/11/15 考試時限(Mins)：100分 試題本文： 1.(50%) The following data give the spot prices ( in US dollars ) of a brrrel crude oil for 14 business days. ------------------------------------------------- 139.96 141.06 143.74 145.31 141.38 136.06 135.88 141.47 144.96 145.16 138.68 134.63 129.43 128.94 ------------------------------------------------- (1) Find the mean and variance for these data. (6%) (2) Construct a frequency distribution table for these data using a class width 3.00 and the lower boundary of the first class equal to 128.00. (6%) (3) Find the mean and variance of the grouped data based on part (2). (7%) (4) Compare your means and variances from parts (1) and (3). Explain why they differ. (4%) (5) Calculate the median and mode for these data. Compare the mean, mode, and median. (5%) (6) Draw a relatively frequency histogram for these data based on part (2). Discuss its shape and compare it with part (5). (6%) (7) Construct a box-andwhisker plot. Compare this plot with part (5) and comment on the skewness of these data. (10%) (8) Determine the percentage of observations that fall within 1.5 standard deviation units from the mean. Do your result support Chebyshev's theroem? (6%) 2.(22%) In a sample survey, 1800 senior citizens were asked whether or not they have ever been victimized by a dishonest telemarketer. The following tabel gives the responses by age group (in year). ------------------------------------------------------------------------------ Have been victimized Have never been victimized 60-69 (A) 106 698 AGE 70-79 (B) 145 447 80 or over (C) 61 343 ------------------------------------------------------------------------------ Suppose one person is randomly selected from these senior citizens. Find the following probabilities: (1) P(have been victimized and C) (4%) (2) P(have never been victimized and A) (4%) (3) P(have been victimized or B) (4%) (4) P(have never been victimized or C) (4%) (5) P(A | have been victimized) (4%) (6) P(B and C) (2%) 3.(15%) A psychologist needs 10 pigs for a study of the intelligence of pigs. She goes to a pig farm where there are 40 young pigs in a large pen. Assume that these pigs are representative of the population of all pigs. She selects the first 10 pigs she can catch and uses them for her study. (1) Do these 10 pigs make a random sample? Why or why not? (4%) (2) Are these 10 pigs likely to be representative of the entire population? Why or why not? (4%) (3) Please suggest a better procedure for selecting a sample of 10 from the 40 pigs in the pen. (7%) 4.(13%) What is the difference between a sample survey and a census? Why can it be advantageous to select a sample instead of carrying out a census? --

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