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110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:統計學(H)#111297

科目：研究所、轉學考(插大)◆統計學 | 年份：110年 | 選擇題數：40 | 申論題數：0

試卷資訊

所屬科目：研究所、轉學考(插大)◆統計學

選擇題 (40)

1. Let = 3600.7 and S2 = 14655 be the sample mean and variance of the weights of nineteen neonates in grams. Suppose that there was a typewriting error in the cighth observation, the accurate weight of eighth neonate, 4320 was recorded as 4230. After we correct it, what are the accurate sample mean and variance (A) Sample mean: 3605.44, Variance: 20274.32 (B) Sample mea an: 3605.44, Varianc ce: 21175.7 (C) Sample mean: 3609.23, Variance: 22437.62 (D) Sample mean: 3609.23, Variance: 23416.3

2. Let A and B be the events such that P( A ) = 0.4, P( B ) = 0.6, and P(AC ∩ BC)=, Then P(AC∪BC) =?,P(AC ∪ BC) =? (A) (B) (C) (D)

3. Suppose that a firn's sales were S2,500,000 four year ago, and sales have grown annually by 1 5%, 15%, -10%, 5% since that time. What was the mean growth rate in sales over the past four years? (A) 6% (B) 17% (C)25% (D) 33%
4. An insurance company believes that people can be divided into two classes - those are accident-prone and those are not. Their statistics show that an accident-prone person will have an accident at some time within a fixed I-year period with probability 0.5, whereas this probability decreases to 0.4 for a non-accident-prone person. If we assume that 40% of the pcpulation is accident-prone, what is the probability that a new policy holder will have an accident within a year of purchasing this policy? (A)0.44 (B) 0.45 (C) 0.46 (D) 0.47

5. Given the probabilities of some of events as follows: P(C|B) =0.95, P(C|BC)=0.3, P(AIB∩ C) = 0.2, P(A|BC∩ C) = 0.05, P(A|B ∩ C) = 0.35, P(AIBC ∩CC)= 0.2.Compute P(A|B). (A)0.2021 (B)0.2075 (C) 0.2098 (D)0.2132
6. A Bayesian approach can be used to revise probubilitis that a prospect field will produce oil. In one case, gcological assessment indicates a 25% chance that the field will produce oil. Furthes, tlere is an 80% chance that particular well will strike oil given that oil is preseat in the prospect filed, Suppose that one well is drilled on the field and it comes up dry. What is the probability that tbe prospect filed will produce oil? (A) 0.0333 (B)0.0425(C)0.0625 (D) 0.0675

7. Suppose we took a pair of randor: samples (X1,X2), with replacement frot: pogulation f(X): Find E() and P(X＞1) (A) E() - 14, P(＞1)=0.50 (B) E () = 1.4, P( ＞1)=0.49 (C) E () =1.6. P(＞1)=0.69 (D) E ()= 1.6, P(＞ 1)=0.71
8. The Sutton police dcpartnent nust write, on average, 6 tickets a day to keep department revenues at budgeted levels. mean of 6.5 tickes per day. Interpret Suppose the number of tickets written per day follows a Poisson distribution with a t the value of the mean. (A) The mean has no interpretation. (B) The expecto ted pumber of tickets writt written would be 6.5 per day. (C) Halt of the days have less tharn 6.5 tickets writen and balf of the days have more than 6,5 tickets written. (D) The number of tickets that is written most often is 6.5 tickets per day.
9. A firm manufactures metal rods which must be rejected if they are not betwecn 6.025 and 6.475 cn in dianeter. The expect value of the diameter of the rods is 6.25 cmn, and the standard dev deviation of tbese diamet eter is 0.035 cm. What is the maximum probability that a rod will be rejected? (A) 0.0531 (B) 0.0444 (C) 0.0357 (D)0.0242

10. Consider tbe infinite population described by the probability distribution show here.
Assume a rindom sumple of n = 80 measurenents is selected from the population, find the sampling distrioution of the sample mean  and calculate P (0.905＜＜1.095) (A) = 1. P(0.905 ＜ ＜ 1.905) =0,7330 (B)= 1, P(0.905＜ ＜1.905) = 0.6578 (C) = 1.2. P(0.905 ＜＜1.905)= 0.7920 (D)= 1.2, P(0.905＜＜ 1.905)=0.9505
11. Suppose that A, B and C are three independent events such that P( A ) = 0.6, P( B ) = 0.4, P( C ) = 0.2. What is the probability that exactly one of these three events will oceur? (A) 0.371 (B) 0.398(C)0.407 (D)0.464

12. If X, Y, Z are pasitive valued and all have means of 5 and standard deviations of 3, estinnate the prooubility that the averuge of X, Y, and Z is less than J0 by Chebyshev's inequality. If X, Y and Z all have correlation coeftieients of 0.3. (A) (B) (C) (D)

13. 1f' the random vuriable X is exponentially distributed, then tbe mean of X will be: (A) greater than the median. (B) less than the median. (C) equal to tbe median. (D) Cannot tell； the answer depends on what λ is.

14. If n = 100 and the number of successes is 49 for a random sample from a binomial population, find the estimates for the variance of the sample proportion of successes (A) 0.0018 (B) 0.0025 (C)0.0033 (D) 0.0049
15. In testing the difference between the means of two normally distributed populations, the nunbet of degrees of freedom associated with the unequa sal-variances t-test statistic usually results in a non-integer number. It is r recommended that you: (A) round to the nearest integer. (B) chunge the sample sizes until the number of degrees of frocdom becomes an inteyer. (C) assume that the population variances are equal, and then use df= n1 + n2 -2 (D) None of these choices.

16. When testing H0:μ1 -μ2 =0 vs. H1=μ1 -μ2≠ 0, the observed value of the z-score was found to be -2.15. Then, the p-value for this test would be (A)0.0158 (B)0.0316 (C)0.9842 (D)0.9684

17. According to Chebyshev's inequality, the probability that in n throws of a fair die the number of fives lies between is greater than or equal to (A) (B) (C) (D)
18. In the NBA final, Lakers and Nets play a sequence of ganes and the first team that wins a total of four gares becomes the champion. If the probability that Lakers rs win a particular game over Nets is 0.6. .What is the probability that Lakers will becomse the champion? (A)0.6102 (B) 0.6307 (C) 0.6934 (D) 0.7102
19. When tbe effect of a level for one factor depends on which level of another factor is present, the most appropriate ANOVA design to use in this situatioo is the: (A) One-way Y ANOVA wi with 2 treatments. (B) Two-fuctor ANOVA with interuction. (C) Two-fuctor ANOVA with no internction. (D) None of these choices

20. A hotel chain has identically size resorts in S locations. Tive data that follow resulted from analyzing tbe Hotel occupancies on randomly selected days in the 5 locations. Analysis of Variance Referring to the above table, the value of the elerner nent in the ANOVA table that always provides an estimate of the population variance is__________.(A)9.16(B)21.0 (C) 240.9 (D) 261.9
  21. A 95% confidence interval estinate can be interpreted to mean that (A) Ifall possible samples of size N are taken and confidence interval estimates are developed, 95% of thems would include tibe true populat tion tean somewhere within their interval. (B) We have 95% confidence that we have selected a sample whose interval does include the he population mean. (C) Both above. (D) None of the above.
22. Suppose a 99% comfidence interval for H turr urs out to be (100, 200). To make more useful inferences from tbe data, it is desired to reduce the width of the confidence interval. Which of the following will esult in a retuced interval width? (A) Incrense the sample size. (B) Increase the confidence level. (C) Increase the population mean. (D) Increase the sample mean. (E) None of the above.
23. Which of the following is not true about tbe Student's t distribution? (A)3t has more area in tbe tails and less in the center than does the normal distribution. (B) It is used to construct confidence intervals for the population nean when tbe population standard deviation is known. (C) It is bell shaped and symmetricnl. (D) As the number of degrees of freedom increases, the t distribution ap approaches the nornal distribution. (E) None of the above.
24. If the p-value is less ehan a in a two-tail test.. (A)the null hypothesis should not be rejected. (B)the null hypothesis should be rejected. (C)a one -fail test should be used. (D)no conclusion should be reached. (E) None of the above.

25.1f the Type I error (a) for a given test is to be decreased, then for a fixed sample size n (A)the Type Il eror (β) will also decrease. (B) the Type Il error (β) will increase. (C) the power of the test will increase. (D)a one-tail test must be utilized. (E) None of the above.

26. Suppose we wish to test H0: μ≤45 versus H1: μ ＞ 45. What will result if we conclude that the mean is grenter than 45 when its true value is really 52? (A) We have made a Type I error. (B) We have made a Type II error. (C) We have made a correet decision (D)None of the above are correct.

27. You have created a 95% confidence interval for p with the result 10 ≤ μ ≤ 15. What decision will you make if we test Ho: p = 17 versus H : μ≠ 17 at a = 0.10? (A)Reject H0in favor of H. (B) Do not reject H0 in favor of H. (C) Fail to reject H0 in fnvor of H. (D) We cannot tell what our dccision will be from tbe inforration given. (E) None of the abowe.
28. Which of the following statements is not true about the level of significance in a bypothesis test? (A)The larger the level of significance, the more likely you are to reject the null hypothesis. (B) The level of significance is tbe maxintum risk we ore willing to socept in making a Type I etror. (C) The significance level is also called the a level. (D) The significance level is another name for Type II error. (E) None of the above.
29. In perforning a regression analysis involving two nuerical variables, you are assuming (A)tbe vari iances of X and Y are equal. (B) tbe variation around the line of regression is the ssme for each X value. (C)that X and Y are independent. (D)All of the above. (E) None of the above.
30. If the correlation cocfficient (r) = 1.00, thetn (A)the Y-intercept (b0) must equal 0. (B) ue explained variation equals the unexplained variation. (C)there is no unexplained variation. (D)there is no explained variation. (E) None of the above.

31. Testing for the existence of corelation is equivalent to (A)testing for the existence of the slope (β1). (B) testing for tbe existence of the Y-intercept (β0) (C)the contidence interval estinate for predicting Y. (D)None of the above,
32. In the regression analysis, the width of the prediction interval for the predicted value of Y is dependent on (A)the standard enor of the estimate. (B) the value of X for which the prediction is being made. (C) the sample size. (D)All of the above (E) None of the above.
33. When the economist used a simple linear regression model with consu umption as the dependdent variable and GDP as the independent variable, be obtained an R2 value of 0.971. What additional percentage of the total variation of consumption has been explained by including gaggregate prices in the rultiple regression? (A)98.2 (B)11.1 (C)2.8(D)1.1 (E) None of the above.
34. What is the predicted consumption level fos an economy with GDP equal to $4 billion and an aggregate price index of (A)$1.39 billion (B) $2.89 billion (C) $4.75 billion (D)$9.45 billion (E) None of the above.
35. What is the estimated mean consumption Jevel for an economy with GDP equal to $4 billion ard an aggregate price index of 150? (A)$1.39 billion (B)$2.89 billion (C)$4.75 billion (D)$9.45 billion (E) None of the above.
36. One cconomy in the sample had an aggregate consumption level of S4 bilion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point? (A)$4.39 billion (B) $0.39 billion (C) -$0.39 billion (D)-$1.33 billion (E) None of the above.
37. To test for the significam mce of the coefficient on aggregnte price index, the p-value is (A)0.0001 (B)0.8330(C)0.8837 (D)0.9999 (E) None of the above.
38. To test whether aggregate price index has a negative imption, the p-value is________?  (A)0.0001 (B)0.4165 (C)0.8330(D)0.8837 (E) None of the above.
39. An interaction tem in a multiple regression model may be used wben (A) the coefficient of determination is small. (B) there is a curvilincar relationship between the dependent and independent variables. (C) neitber one of 2 independent variables contribute significantly to the regression model. (D)the relationship between X1and Y changes for differing values of X2. (E) None of tbe above.
40. A microecon onomist wants to detern to determine how corponte sa sales are intluenced by capital and wage spen ending by com mpanies. She proceeds to randomly select 26 large corporations and record infonnation in millions of dollars. A statistical analyst discovers that capital spending by corporations has a significant inverse relationship with wage spending. What should the microeconomist who developed this multiple regressian aodel be particularly concered with? (A) Randoa bmness of' error terims (B) Collinearity (C) Normality of residuals (D) Missing obscrvations (E) None of the above. 

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