110年 - [非官方正解]110 國立中山大學_碩士暨碩士專班招生考試_企管系企管甲班/甲、乙、丙組選考:商用統計學#104450

科目：研究所、轉學考(插大)◆商用統計學 | 年份：110年 | 選擇題數：18 | 申論題數：5

試卷資訊

所屬科目：研究所、轉學考(插大)◆商用統計學

選擇題 (18)

複選題
1. Which of the following is/are included in the field of statistics? (A) Collecting data；(B) Analyzing data； (C) Presenting data； (D) Interpreting data； (E) None of above.
複選題
2. Which of the following descriptions is/are INCORRECT? (A) "Phone number" is a nominal variable； (B) "Temperature in Celsius" is a ratio variable； (C) "Cancer stage" is an interval variable； (D) "Height in centimeter" is a discrete variable； (E) "Age group" is a categorical variable.
複選題
3. Which of the following is/are NOT used to measure central location? (A) Arithmetic mean； (B) Interquartile range； (C) Mode； (D) Standard deviation； (E) Midrange.
複選題
4. Which of the following is/are correct? (A) A "scatterplot" is good for obtaining the potential association between two numerical variables； (B) Unlike "bar graph", a "histogram" has no natural separation between rectangles of adjacent classes； (C) A "pie chart" is good for comparing the means of a numerical variable between two independent groups； (D) In a "Box-plot", the line drawn in the box indicates the location of the mean； (E) "100% stacked area chart" can be used to compare the change in distribution of a categorical variable over a period of time.
複選題

5. Iftwo events X and Y are independent, which of the following conditions is/are satisfied? (A) P(Y|X)=P(Y)；(B) P(Y|X)=P(X)； (C) 61aeb7143cdb0.jpg-P( A )+P( B )； (D) 61aeb7413803d.jpg=P( A )●P( B  )；(E) None of above.
複選題
6. Assume the following conditions in Taiwan: 10% of undergraduate students study abroad as part of their education. 60% of the undergraduate students who study abroad are female and 50% of the undergraduate students who do not study abroad are female. Which of the following is/are correct: (A) Given a female undergraduate student, the probability that she studies abroad is 11.76%； (B) The overall percentage of female undergraduate students is 51%； (C) The overall percentage of male undergraduate students is 50%； (D) Given a male undergraduate student, the probability that he studies abroad is 4%；(E) Given the undergraduate students who study abroad, the probability of male is 8.16%.
複選題
7. Which of the following belongs to continuous probability distributions? (A) Normal probability distribution； (B) Poisson probability distribution； (C) Binomial probability distribution； (D) Exponential probability distribution； (E) Chi-square probability distribution.
複選題
8. Let P[Y=x] indicate the probability of a sum of x when rolling three dice. Which of the following is/are correct? (A) P[Y=18]=1/2163 (B) P[Y=17=3/216； (C) PY=1]=1/216； (D) P[Y=3]=3/216； (E) PY＜5]=4/216.
複選題
9. Cars arrive at a car wash service randomly and independently. The probability of an arrival is the same for any interval of equal length. The mean arrival rate is 4 cars per 10 minutes. Which of the following is/are correct? (A) The probability that less than 2 cars will arrive during any given 10 minutes of operation is 0.0916；(B) The probability that 5 or more cars will arrive during any given 10 minutes of operation is 0.7815； (C) The probability that more than 6 cars will arrive during any given 10 minutes of operation is 0.1107； (D) The probability that exact 9 cars will arrive during any given 10 minutes of operation is 0.0550； (E) The variance of the arrival rate per 10 minutes is 4.
複選題
10. Suppose that the mean daily TV viewing time per household follows a normal distribution with a mean of 5 hours and a standard deviation of 2 hours. Which of the following is/are correct? (A) The probability that a household views TV more than 3 hours a day is 0.1587； (B) The probability that a household views TV between 4-7 hours a day is 0.5328； (C) In order to be in the bottom 10% of all TV viewing households, a household has to view TV for less than 2.44 hours a day； (D) Among a group of households that all members are obese (BMI>=35), we randomly selected a sample of 16 households to investigate whether the mean of their TV viewing time is longer than that of the population mean. We found that the sample mean was 6.5 hours. To conduct a one-tailed z-test with a-0.05, the z-score=3.(E) From ( D ), we can conclude that households with all obese members have longer TV viewing time than the population with the p-value=0.0013, based on the one-tailed z-test.
11. Rejecting a null hypothesis when the null hypothesis is false is called: (A) Type I error； (B) Type II error； (C) Type III error； (D) power； (E) confidence limit.
複選題
12. In which occasions can we apply a Chi-square test for statistical testing? (A) Test the association between two categorical variables； (B) Test for goodness of fit； (C) Test whether a sample variance is different from the population variance； (D) Test whether sample variances from two groups are different； (E) Test whether sample means from three groups are different.
複選題

13. Consider the following hypothesis test: H0: H=18； Ha:μ≠18. A sample of 36 provided a sample mean of 17 and a sample standard deviation of 3. Which of the following is/are correct? (A) The computed test statistic is -2； (B) The degree of freedom is 17； (C) The p-value ＜0.05； (D) At a=0.05, the critical values are±1.96 for the statistical testing； (E) At o=0.05, do not reject the null hypothesis.
複選題
14. Which of the following is/are NOT correct about ANOVA? (A) One assumption of ANOVA is that all samples are drawn independently； (B) One assumption of ANOVA is that the variances of the populations are equal； (C) Suppose four groups are compared, the null hypothesis is μ1 = μ2= μ3 = μ4, while the alternative hypothesis is μ1# μ2# μ3 # μ4； (D) One-way ANOVA is a one-tailed test, while two-way ANOVA is a two-tailed test； (E) If the test result is not to reject the null hypothesis, we must perform a post-hoc test to confirm that these groups are truly no different from each other.
15. Suppose you got data of "Hight in centimeter" and "Weight in kilogram" from all students in an elementary school and you want to investigate the association between the height and weight. Which of the following is/are NOT appropriate? (A) Conduct a line chart to visualize their association； (B) Estimate a correlation coefficient, which ranges from -1 to +1； (C) Conduct a t-test to compare whether height and weight are statistically different； (D) Develop a simple linear regression model and detect whether the slope is significantly different from 0； (E) Estimate the coefficient of determination from the simple linear regression model.
複選題

16. A survey was conducted among mid-sized and small-sized enterprises in Taiwan to investigate their employment plan ("Add Employees", "No Change", or "Lay-off Employee") in Year 2021. The table below summarizes the observed result and its expected value (in the parenthesis) for each cell:
61aeb859c3a5c.jpg Which of the following is/are correct? (A) The expected value of mid-sized companies responding to "Add Employees' is 20； (B) The degree of freedom is 6； (C) The Chi-squared statistic is 16.67； (D) The p-value＜0.001； (E) Given a=0.05, we conclude that there is an association between the size of company and its employment plan. 30(?) 20(?)
複選題
17. Which of the following descriptions is/are correct about forecasting? (A) A Naive forecasting method is done without considering any historical data； (B) When a positive trend exists, the forecasting using moving average method tends to underestimate the true values. (C) In a simple exponential smoothing method, a higher smoothing factor increases the level of smoothing, making the forecast less responsive to recent changes. (D) By treating time as the independent variable and the time series as a dependent variable, regression analysis can be used as a time series method. (E) Time series decomposition can be used to separate or decompose a time series into seasonal, trend, and irregular (error) components.
複選題
18. A survey with size of 150 was conducted to investigate whether gender (male versus female) is associated with annual salary (the dependent variable), after controlling for years of experience, years of education, and the position level categorized as "top or middle level manager', "first-line manager", and "non-manager". You want to conduct a multiple linear regression model. Which of the following is/are correct? (A) When testing for the overall significance of the model, the degree of freedom for the critical value of F is (6, 143)； (B) Assuming that we treat "male" as a reference group for the gender variable, the estimated coefficient is interpreted as the additional amount of women's annual salary compared with male's, after years of experiences, years of education, and the position level are held constant； (C) To test whether years of education is significant factor on annual salary after adjusting other variables, we can use t-test with a degree of freedom of 144 to detect whether its estimated coefficient is different from 0； (D) Given that the 95% confidence interval of the coefficient for years of experience is (500, 1000), its estimated coefficient is definitely a positive value； (E) The variable of "position level" has to be converted to a numerical variable by assigning "non-manager" as O, "first-line manager" as 1, and "top or middle level manager" as 2 in order to be included in the regression model.

申論題 (5)

 1. What is the value of ①?

2. What is the value of②?

3. What is the value of ③?

4. What is the value of ④ (the critical value for statistical testing)?
5. Based on the information above, is there a statistical difference in hours between breakdowns among three machines at a=0.05? (Please answer "yes", "no", or "not enough information")