私立中原大學八十八學年度研究所招生考試命題紙

所組別 :企業管理學系甲組
國際貿易學系甲組
國際貿易學系乙組 		科目 :統計學 考試時間 : 05月01日第4節

一. 單選題: (每題3分, 共45分)
  1. The standard deviation (denoted by s) of a set of sample scores is a measure of variation calculated by the following formula :

    　
  2. According to Chebyshev's Theorem, the proportion (or fraction) of a set of data lying within 4 standard deviations of the mean is always at least
    1. 14/16.
    2. 15/16.
    3. 12/16.
    4. 1/16.

    　
  3. A multiple regression equation expresses a linear relationship between
    1. two or more dependent variables and one independent variable.
    2. one dependent variable and two or more independent variables.
    3. two dependent variables and two or more independent variables.
    4. none of the above.

    　
  4. The expected value of a Chi-Square Distribution with sample size n = 20 is
    1. 20.
    2. 40.
    3. 19.

    　
  5. When estimating a multiple regression model, if one gets a high R but very few significant t values for the coefficients estimated, then there is a possibility of
    1. multicollinearity.
    2. homoscedasticity.
    3. heterscedasticity.
    4. linearity.

    　
  6. If the value of coefficient of determination is close to 1 in a regression model, then it implies that
    1. the estimated model is not linearly related.
    2. the estimated coefficients are all significant.
    3. the estimated regression line fits the data well.
    4. the model has a dummy variable.

    　
  7. When conducting a hypothesis test for the population mean with sample size of 25, we may use
    1. Z test.
    2. F test.
    3. χ2 test.
    4. t test .

    　
  8. When a nonstandard normal distribution N(130, 15) is converted to a standard normal distribution, if we know the population mean is 100 and the standard derivation is 15, then the Z score is
    1. 30.
    2. 1.
    3. 2.
    4. 3.

    　
  9. A type II error is the mistake of
    1. rejecting a true null hypothesis.
    2. failing to reject a false null hypothesis.
    3. accepting a true null hypothesis.
    4. rejecting a false null hypothesis.

    　
  10. If we are performing a hypothesis test for the population variance, the statistics we use is
    2. s2 /σ2.
    3. (n-1)s2/σ2
    4. none of the above.

    　
  11. The power of a test is the probability that the test will correctly lead to the rejection of the null hypothesis. If type II error is β=0.13 and the type I error is 0.05, the power of a test is
    1. 0.95.
    2. 0.87.
    3. 0.05.
    4. 0.13.

    　
  12. If we want to test for the difference between the means of two independent samples with samples of n1 = 25 and n2 = 25, the number of degrees of freedom is equal to
    1. 50.
    2. 49.
    3. 48.
    4. 25.

    　
  13. According to the Central Limit Theorem, the distribution of sample means will, as n increases, approach a normal distribution with mean μ and standard deviation shown as
    1. σ.
    2. s.

    　
  14. Which of the following tests is used to detect the problem of autocorrelation in the time series data?
    1. a Chi-Square test.
    2. an F test.
    3. the Goldfeld-Quandt test.
    4. the Durbin Watson test.

    　
  15. If two events A and B are mutually exclusive, the probability of a union of the two events is equal to
    1. P(A) + P(B).
    2. P(A) + P(B) - P(A∩B).
    3. P(A∩B)/ P(B).
    4. none of the above.

    　

二. 填充題: (每一空格3分, 共30分)
  1. If y is a random variable that possesses a uniform distribution with Θ1 and Θ2 , then the expected value of y is _________ and the variance of y is __________.

  2. Two samples are _____________ if the sample selected from one population is not related to the sample selected from the other population.

  3. If 51 observations are used to estimate a regression line, and the result is shown as　　with the coefficient of determination R2 =0.8. When we are trying to use more independent variables in the model shown as　　then the adjusted R2 is _______________.

  4. If the price of a farm land is estimated by performing a multiple regression model, the results are as follows:
    ln (P) = 9.14 + 0.25 ln (S) - 0.54 ln T + 0.33 (Tr)
    where
    P=price, S=size, T=tax,
    Tr=dummy variable, Tr=1 if tree planted, Tr=0 if no trees.
    Then, if the government increases tax by 1%, will ________ the price of by ________. If trees are planted, the price of land will ______________ by _____________.

  5. From the following ANOVA table, the calculated F-ratio is ____________.
    ANOVA
    ________________________________________________________________
    SSdf
    ________________________________________________________________
    SSB683
    SSE9418
    ________________________________________________________________
    SST16221
    ________________________________________________________________

  6. Given the discrete random variable y and its probability function as follows:
    y　　　　-1　　　　0　　　　1
    P(y)　　0.1　　　0.3　　　0.6

    Then the expected value of y, E(y) is _____________.

三. 計算題: (第一題15分, 第二題10分, 共25分)
  1. The engineering department of a car manufacturer claims that the fuel consumption rate of one model is equal to 35 miles/gal. The quality control group suggests that σ=4 miles/gal, and a sample of 50 cars yields =33.6 miles/gal. Given Z0.025=1.96. Test the claim of the engineering department using a 0.05 level of significance.　　(15分)

  2. Annual data from 1963 to 1990 were used to develop two different forecasting models. The forecasted and actual values for these years are shown in the following table. Use mean absolute deviation (MAD) and sum of squares for forecast error (SSE) to determine which model performed better. (10分)

    Forecast value
    Year　　　Actual value of y　　　model 1　　　model 2
    _____________________________________________________________________
    1991　　　　　　　　129　　　　　136　　　　　118
    1992　　　　　　　　142　　　　　148　　　　　141
    1993　　　　　　　　156　　　　　150　　　　　158
    1994　　　　　　　　183　　　　　175　　　　　163
    _____________________________________________________________________


--- END---