110年 - [非官方正解]110 國立臺灣大學_碩士班招生考試_財務金融研究所甲、丙組:商用統計學#105747

科目：研究所、轉學考(插大)◆商用統計學 | 年份：110年 | 選擇題數：10 | 申論題數：8

試卷資訊

所屬科目：研究所、轉學考(插大)◆商用統計學

選擇題 (10)

1. Firm size (Size) is measured in million dollars. If you change the unit of measurement to billion dollars. What will be the new estimated coefficient of Size? (A)61de663c64611.jpg (B) 61de665af0b6f.jpg (C) 0.4 x 103 (D)0.4✖103 (E)None of the above choices (a)-(d).
2. Ho: The coefficient of BM is zero. Ha: The coefficient of BM is not zero. You test H0 using a t-test, with the test statistic = 2.36. Probability(t-statistic ＞ 2.36)-0.0091. Which of the following is correct? (A) You can reject H0 at the 10% level, but no ot at the 5% level. (B) You can reject H0 at both the 10% and 5% leve (C) You can reject H0 at the 10%, 5% level, and 1% levels. (D) You cannot reject H0 at the 10%, 5% level, or 1% level. (E) None of the above choices(a)-(d).

3. IfX1，X2, .... Xn are mutually independent normal random variables, with their means all equal to 3 and variances equal to 10, what is the variance of Y =61de674c4a354.jpg?(A)400 (B) 200 (C) 400n (D) 200n (E) None of the above choices (a)-(d).

4. Y is distributed 61de67a65de9a.jpg, and K is distributed 61de67c624a2a.jpg. Suppose Probability(Y S 16) = 0.90. Please calculate Probability(K ≤ 1.6). (A) 0.09(B)0.45(C) 0.75 (D)0.90  (E) None of the above choices (a)-(d).

5. A random draw (with replacement) of 1000 balls from a pool of several million balls is conducted. Each ball is cither blue or red. Let p denote the fraction of blue balls in the population. Let 61de680958c71.jpg denote the fraction of blue balls in the sample. You want to test the competing hypotheses H0: P = 0.4 vs. H1: P ≠0.4. Suppose that you decide to reject 61de686b6e58a.jpg Note that the sample of l 000 balls is considered as a large sample. What is the type I error of this test? (A)0.178 (B)0.256(C)0.367 (D) 0.488 (E) 0.519

6. Suppose you estimate a sample OLS regression model. The resulted regression equation is: Yi = 4.1 + 3.5 Xi +εi.Yi， Xi, and εi denote the dependent variable, independent variable, and the regression residual, respectively: indexes cach individual observation. If X, is equal to 2, what is the predicted value of Yi?(A)23.5 (B) 19.6 (C) 15.2 (D) 11.1 (E) None of the above choices (a)-(d).

7.Suppose a population regression model is: Yi =β0 + B1Xi + ui. Yi, Xi, and ui denote the dependent variable, independent variable, and the error term, respectively. i indexes each individual observation. 61de699e5447f.jpg are the OLS estimators, and 61de69c6e7787.jpg is the regression residual, using a sample of n observations. Which of the following statement is false? (A)61de69f1b0863.jpg (B)61de6a18f02a1.jpg (C)Suppose 61de6a459b207.jpg and the correlation between Xi and ui is zero. Then, the OLS estimator 61de6a871aebd.jpg is inconsistent. (D) The assumption that the correlation between Xi and ui is zero cannot be tested empirically. (E) None of the above choices (a)-(d)

8. In Equation 2, holding all other factors constant, when Total.Assets increases by 1%, what is the predicted change in Earnings? (A) Increase by 250 dollars. (B) Increase by 1284 dollars. (C)Increase by 0.25%. (D) Increase by 25%. (E) None of the above choices (a)-(d).
9. Suppose Equation 2 is the correct model. That is, a firm's total asset size is a determinant of an employce's earnings. Are larger firms (measured by total asset size) more likely than smaller firms to employ college graduates? (A) Larger firms are more likely to hire college graduates. (B)  Smaller firms are more likely to hire college graduates. (C) All sizes of firms are equally likely to hire college graduates. (D) We don't have sufficient information to answer this question. (E) None of the abo bove choices (a)-(d).
10. Which of the following is false? (A) If all Gauss-Markov conditions are satisfied, the OLS estimators are unbiased. (B) If all Gauss-Markov conditions are satisfied, the OLS estimators are consistent. (C) If all Gauss-Markov conditions are satisfied, the OLS estimators have the lowest conditional variance among all linear conditionally unbiased estimators. (D) Ifthe conditional variance of ui is heteroscedastic, then Gauss-Markov conditions are violated and the OLS estimators are biased. (E) None of the above choices (a)-(d).

申論題 (8)

1. A recent report claims that college non-graduates get married at an earlier age than college graduates. To support the claim, tandom samples of size 100 were selected from each group, and the mean age at the time of marriage was recorde(D) The mean and standard deviation of the college non-graduates were 21.6 years and 3 years, respectively, while the mean and standard deviation of the college graduates were 23.2 years and 4 years, respectively. To test the claims of the report at the 0.05 level of significance, the figure of the appropriate test statistic is__________.

2. Let the joint probability function of X and Y be given by
61de6bf7cb825.jpg
 P(X=1|Y=2)=_________.
3. Customers enter a restaurant at random at a rate of four per minute. Assume that the number entering this restaurant in any given time interval has a Poisson distribution. The probability that at least two customers enter the restaurant in a given 0.25-minute interval is__________.
4. A random variable X represents the number of defective mobile phone is a shipment of four iPhones to a local mobile phone store. Assume that each mobile phone is equally likely to be defective or non-defective, and also assume that each mobile phone is defective or non-defective independently of the other mobile phones. Then the expected number of defective mobile phones is_________.

5. Suppose that a firm's sales region has been divided into five territories, each of which was judged to have an equal sales potential. The actual sales volume for several sampled days is indicated below. 61de6c69e6517.jpg
 If the manager of the firm wants to test the significance of the difference between the observed and expected levels of sales, the figure of the appropriate test statistic is_________.

6. The time elapsed, in minutes, between the placement of an order of pizza and its delivery is random with the density function
61de6cad4c5d0.jpg
Suppose that it takes 15 minutes for the pizza shop to bake pizza once the shop receives the order. The mean of the time it takes for the delivery person to deliver pizza is___________.

7. The following time series represents sales of imported cars in a city for the years 20I I through 2017:
61de6cefd902c.jpgSuppose we e want to estimate annual sales of imported cars in the year 2018. The expected number of imported car sales is____________.

8. A manufacturer produces a special alloy steel with an average tensile strength of 26,000 psi. A change in the composition of the alloy is said to increase the breaking strength but not affect the standard deviation which is known to be 400 psi. The manufacturer wants to conclude that the tensile strength has increased only if he is 99% sure of this (c = 0.01). If the average tensile strength is increased by as much as 300 psi, the manufacturer wants to err by not detecting the change at most 10% of the time (β = 0. 10). Assume that the z statistic with respect to the type I error is 2.33 and the z statistic with respect to the typeⅡerror is -1.28. The required sample size to meet these conditions is___________.