課程名稱︰心理及教育統計學上 課程性質︰必修 課程教師︰姚開屏 開課學院：理學院 開課系所︰心理系 考試日期（年月日）︰2008-12-12 考試時限（分鐘）：70+90 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Part I. Close book 【15 items, 4 points each, total = 60 points + 6 points for bonus items】 9:10 ~ 10:20 AM 1.What is "point estimation"? What is "interval estimation"? 2.Please interpret why "hypothesis testing" is equivalent to "interval esti- mation". (Please try to prove it.) 3.What are the six steps for conducting hypothesis testing? 4.Please give examples of "Type I error" and "Type II error". (You cannot use the examples from Friday lectures.) 5.What is "p-value"? What is the relationship between p-value and α under hypothesis testing? 6.What is "Bernoulli trial"? What is "binomial distribution"? 7.What can the Bayes theorem tell us? 【Hint: the purpose of Bayes theorem】 8.What is "independent events"? What is "exhaustive events"? Please also pro- vide the corresponding "laws" that apply to them. 9.What is the purpose of "residual analysis" under categorical data analysis? 10.What are the assumptions of chi-square tests? 11.What are the three types of hypothesis testing the chi-square tests can do? 12.Please compare "Coehn's kappa" and "percentage of agreement". 13.What are the advantages/disavantages of contingency coefficient and Cramer's phi? 14.Prood：If two events are statistically independent, their conditional pro- bability is equal to unconditional probability. 15.Refer to the folloing table, please interpret why the expected value for the left-up cell (with frequency A) would be (A+B)(A+C)/N. ┌───┬───┐ │ A │ B │ A+B ├───┼───┤ │ C │ D │ C+D └───┴───┘ A+C B+D N=A+B+C+D Bonus：【6 points】： 1.Please write out the mathematical formula of mormal distribution.【3 points】 σ^2 2 2.Proof： S^2 ~ ──── X 【3 points】 N-1 N-1 Part II. Open book 【40 points】 10:30 ~ 12:00 AM 【For all the following questions, please remember to write out null hypothe- sis, alternative hypothesis, test statistic, critical value, and conclosion. Please use α=0.05】 1.The following table was obtained from 2000 USA General Survey, cross class- fied gender and political party identification. Subjects indicated whether they identified more strongly with the Democratic or Republican party or as Independents. ┌─────┬──────┬──────┬─────┐ │ Gender │ Democratic │Independent │Republican│ Total ├─────┼──────┼──────┼─────┤ │ Females │ 762 │ 327 │ 468 │ 1557 ├─────┼──────┼──────┼─────┤ │ Male │ 484 │ 239 │ 477 │ 1200 └─────┴──────┴──────┴─────┘ Total 1246 566 945 2757 A. Please conduct a test of independence and make conclusion. B. Do residual analysis and interpret. C. Please ignore gender difference. According to the past statistics, the percentage of the USA population on political party identification was 50%(D),15%(I), and 35%(R). Please do goodness-of-fit test on the data and make conclusion. D. Please calculate contingency coefficient and Cramer's phi. 2.When drinking tea, someone claimed that she could distinguish whether milk or tea was added to the cup first. To test her cliam, her friend designed an experiment in which she tested eight cups of tea. Four cups had milk added first, and the other four had tea added first. She was told there were four cups of each type and she should try to select the four that had milk added first. The cups were presented to her in random order. Can we believe her claim? ┌───────┬──────────┐ │ │ Guess Poured First │ ├───────┼────┬─────┤ │ Poured First │ Milk │ Tea │ Total ├───────┼────┼─────┤ │ Milk │ 3 │ 1 │ 4 ├───────┼────┼─────┤ │ Tea │ 1 │ 3 │ 4 └───────┴────┴─────┘ Total 4 4 8 3.In a five-choice task, subjects are asked to choose the stimulus that the experimenter has arbitrarily determined to be correct; the 10 subjects can guess only on the first trial. A. Plot the sampling distribution of the number of correct choice on trial 1. B. What would you conclude if 6 of 10 subjects were correct on trial 1? C. What is the minimum number of correct choices on a trial necessary for you to conclude that the subjects as a group are no longer performing at chance levels? D. What would you conclude if the experiment was conducted on 100 subjects and 60 subjects were correct? ╭ N ╮ Please use the following Binomial probabilities : │ │p^r q^(N-r) ╰ r ╯ ───┬───────────── p ─────────────── N r│ .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 ───┼───────────────────────────── 10 0│ .5987 .3487 .1969 .1074 .0563 .0282 .0135 .0060 .0025 .0010 1│ .3151 .3874 .3474 .2684 .1877 .1211 .0725 .0403 .0207 .0098 2│ .0746 .1937 .2759 .3020 .2816 .2335 .1757 .1209 .0763 .0439 3│ .0105 .0574 .1298 .2413 .2503 .2668 .2522 .2150 .1665 .1172 4│ .0010 .0112 .0401 .0881 .1460 .2001 .2374 .2508 .2384 .2051 │ 5│ .0001 .0015 .0085 .0264 .0584 .1029 .1536 .2007 .2340 .2461 6│ .0000 .0001 .0012 .0055 .0162 .0368 .0689 .1115 .1596 .2051 7│ .0000 .0000 .0001 .0008 .0031 .0090 .0212 .0425 .0746 .1172 8│ .0000 .0000 .0000 .0001 .0004 .0014 .0043 .0106 .0229 .0439 9│ .0000 .0000 .0000 .0000 .0000 .0001 .0005 .0016 .0042 .0098 10│ .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0001 .0003 .0016 4.Refer to Question 1: _ _ A.What is the probability of males and no party identification (i.e. D and R) B.Given males, what is the probability of no party identification? (please use 2 approaches to answer this question : conditional probability and Bayes theorem) C.Compare item A and B and make conclusion. --

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