課程名稱︰統計學下 課程性質︰大二必修 課程教師︰雷立芬 開課學院：管院 開課系所︰國企系 考試日期（年月日）︰2009/4/15 考試時限（分鐘）：三小時 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(15%)To compare the wearing of two types of automobile tires, 1 and 2, an experimenter chose to "pair" the measurements, comparing the wear for the two types of tires on each of 7 automobiles, as shown below. Determine whether these data are sufficient to infer at the 10% significance level that the two population means differ. ┌─────┬─┬─┬─┬─┬─┬─┬─┐ │Automobile│1 │2 │3 │4 │5 │6 │7 │ ├─────┼─┼─┼─┼─┼─┼─┼─┤ │Tire 1 │8 │15│7 │9 │10│13│11│ │Tire 2 │12│18│8 │9 │12│11│10│ └─────┴─┴─┴─┴─┴─┴─┴─┘ 2.(15%)A food processor wants to compare two preservatives for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with preservative A and 16 are treated with preservative B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below. Determine whether these data are sufficient to conclude that the average number of hours until spoilage begins differ for preservative A and B. (α=.05) ┌───────┬───────┐ │Preservative A│Preservative B│ ┌─────────────┼───────┼───────┤ │Sample Mean │108.7 hours │98.7 hours │ ├─────────────┼───────┼───────┤ │Sample Standard Deviation │10.5 hours │13.6 hours │ └─────────────┴───────┴───────┘ 3.(8%)A quality control inspector keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2? ┌────────┬─────────────┐ │Production line │Acceptable Unacceptable │ ├────────┼─────────────┤ │1 │152 48 │ │2 │136 54 │ └────────┴─────────────┘ 4.A partial ANOVA table in a randomized block design is shown below, where the treatments refer to different high blood pressure drugs, and the blocks refer to different groups of men with high blood pressure ┌──────────┬───────────┐ │Source of Variation │SS df MS F│ ├──────────┼───────────┤ │Treatments │a 4 d f│ │Blocks │3,120 6 e g│ │Error │b c 115 │ ├──────────┼───────────┤ │Total │12,600 34 │ └──────────┴───────────┘ a)Fill in the missing values(a-g) in the above ANOVA table.(7%) b)Can we infer at the 5% significance level that the block means differ?(5%) c)Can we infer at the 5% significance level that the treatment means differ? (5%) 5.(10%)The personnel manager of a consumer products company asked a random sample of employees how they felt about the work they were doing. The following table gives a breakdown of their responses by age. Is there sufficient evidence to conclude that the level of job satisfaction is related to age? Use α=.10 ┌─────────────────────────────────────┐ │ Responses │ ├─────────┬───────────────────────────┤ │Age │Very Interesting Fairly Interesting Not Interesting │ ├─────────┼───────────────────────────┤ │Under 30 │31 24 13 │ ├─────────┤ │ │Between 30 and 50 │42 30 4 │ ├─────────┤ │ │Over 50 │32 21 3 │ └─────────┴───────────────────────────┘ 6.(10%)Suppose that a random sample of 60 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardized and the number of observations in each of the intervals below was counted. Can we infer at the 10% significance level that the data were drawn from a normal population? ┌─────┬─────┐ │Intervals │Frequency │ ├─────┼─────┤ │Z≦-1 │8 │ │-1＜Z≦0 │30 │ │0＜Z≦1 │17 │ │Z＞1 │5 │ └─────┴─────┘ 7.(10%)The marketing manager of a pizza chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of pizza parlors, hamburger emporiums, and fast-food chicken restaurants are different. As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below. From previous analysis we know that the ages are not normally distributed. Do these data provide enough evidence at the 10% significance level to infer that there are differences in ages among the customers of the three restaurants? ┌──────────────┐ │ Customers' Age │ ├──────────────┤ │Pizza Hamburger Chicken │ ├──────────────┤ │ 23 26 25 │ │ 19 20 28 │ │ 25 18 36 │ │ 17 35 23 │ │ 36 33 39 │ │ 25 25 27 │ │ 28 19 38 │ │ 31 17 31 │ └──────────────┘ 8. A high school student, who started doing photography as a hobby, is considering going into the photography business. The anticipated payoff table is shown as follows. The following prior probabilities are assigned to the states of nature: P(poor)=0.4, P(fair)=0.4, and P(super)=0.2. Alternative State of nature Start Do Not Start new business new business ┌───────────────┐ poor │ -$12,000 0 │ │ │ Fair │ $10,000 0 │ │ │ Super │ $15,000 0 │ └───────────────┘ a) Determine the EMV decision. (7%) b) What is the expected payoff with perfect information? (3%) c) What is the expected value of perfect information? What does it mean? (5%) *可帶一張雙面A4大抄、計算機、字典 *有附Z, p, t, F, χ^2等數值，若要的值沒有可以問助教 --

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