世新大學九十一學年度碩士班招生考試試題

系所別

考試科目

財務金融學系碩士班

統計學

 

※    考生請於答案卷內作答

請寫出過程，否則以零分計算！

1. （20％）Let A1 denote the event that a part is from supplier 1 and A2 denote the event that a part is from supplier 2. Currently, 65% of the parts purchased by the company are from supplier 1 and the remaining 35% are from supplier 2. Historical data suggest that the quality ratings of the two suppliers are shown in the following table.

                        

   Percentage           Percentage

                                                Good Parts           Bad Parts

 


Supplier 1            98                   2

                                  Supplier 2            95                   5

            

    Suppose now that the parts from the two suppliers are used in the firm’s manufacturing process and that a machine breaks down because it attempts to process a bed part. Given the information that the part is bad, what is the probability that came from supplier 1?

2. (20%) In 1991, the average interest rate charged by U.S. credit issuers was 18.8 percent. A financial officer wishes to study whether the increased competition in the credit card business has reduced interest rates. In order to carry out this project, the officer randomly selects a sample of 15 credit cards and finds their mean interest rate is x  = 16.827% with corresponding standard deviation being s = 1.538%. At 1% significance level (the critical value is – 2.624), what would by your conclusion?

3. (20%) Is the type of beverage ordered with lunch at a restaurant independent of the age of the consumer? A random poll of 309 lunch customers is taken, resulting in the following contingency table of observed values.

                               

Preferred Beverage

                                           Coffee/Tea       Soft Drink         Other

                            21 – 25        26                     95               18

                 Age     35 – 55        41                    40                 20

                              >55           24                     13                 32

 

Use 1% significance level (the critical value is 13.276) to determine whether the two variables are independent.

4. Suppose that we have the following regression,

                yi = βx +ei

and the data set as,

                        yi        1        2       0

                        xi        2       1       0

 

a.       (10%) Please estimate the β parameter by least squares approach.

b.      (10%)What is R2? Calculate the R2 of the regression.

5. Let yi denote the starting salary of college graduates and we have the following regression result,

                                                (1)

   where the dummy variable is defined as,

 

               

a.       (10%) What is the meaning of the estimate ‘6’ (the coefficient of d1i) in equation (1)?

b.      (10%) If we re-define another dummy variable d2i as follows,

  

     then, equation (1) can be re-formulated as

                  

     What are the estimates of  and  , respectively?