QUANTITATIVE TECHNIQUES FOR MANAGEMENT-KANNUR UNIVERSITY

I Semester M.B.A. Degree (Reg./Supple.) Examination, January 2015
  MBA1C  03 :QUANTITATIVE TECHNIQUES FOR MANAGEMENT
                                                  (2014 Admn .)


                                                   SECTION-
 Answer two questions in this Section. Each questions carries 13 marks1
1 a)A studyby the Atlanta,Georgia, Department of Transportation on the effect of
      bus ticket  prices on the number of passengers produced the following results :
          Ticket
           price (Rs.)     25   30  35  40  45  50  55  60
     _____________________________________________
          Passenger
          per 100 miles 800  780  780  660  640  600  620  620
    ______________________________________________
      Develop the regression equation and predict the number of passengers per
      100 miles if the ticket price were 50 Rupees.
                                         OR
  b)  Fluctuation in this daily sales of two products, Xand Y, are given  below. Find
out which of the two products shows greater fluctuation in sales.
       Daily sales for product X : 620, 624, 622 ,625, 622, 618, 619, 616, 623, 625,
       626 and 625.
       Daily sales for product Y : 2152, 2134, 2132, 2145, 2132, 2142, 2146, 2130,
       2146, 2142,      2150, 2135, 2152.
2.a) A research company has designed three different systems to clean up oil
       spills. The following table contains the results, measured by how much surface
       area (in square meters) is cleared in 1 hour. thus data were found by testing
       each method in several trails. Are the three systems equally effective ? Use
       0.05 level of significance.
System A           55     60          63       56       59       55
System  B          57     53          64       49       62       -
System C           66     52          61       57       -          -
                                      OR
b) Describe the probability sampling techniques and its application in business
    research.
                                           SECTION-B
Answer any six questions in this section. Each question carries 1 mark for
part(a), 3 marks for part(b), and 5 marks for part(c).
3.  a) What do you mean by equally likely ?
     b) Explain the relevance of probability theory to management decisions.
     c) In a production run of 500 items, 15 items are found to be defective.If the one
        item is drawn from the production run at random, What is the probability that it
       will be found defective ? Comment on your result.
4.  a) What is a point estimate ?
     b) Explain briefly the criteria of a good estimator.
     c) When a sample of 70 retail executives was surveyed regarding the poor
         November performance of the retail industry, 66 percent believed that
        decreased sales were due to unseasonably warm temperatures, resulting in
        consumer's delaying purchase of cold weather items.
       Estimate the standard error of the proportion of retail executives who blame
       warm weather for low sales.Find the upper and lower confidence limits for
       this proportion, given a 95 percent confidence level.
5.  a) What is null hypothesis ?
     b) Explain type I and type II error.
     c) A personnel specialist of a major corporation is recruiting a large number of
        employees for an overseas assignment. During the testing process,
       management asks how things are going, and she replies, "Fine. I thing the
      average score on the aptitude test will be around 90." When the management
      reviews 20 of the test results complied, it finds that the mean score is 84, and
     the standard deviation of this score is 11. The management wants to test
    whether the true score is smaller than the hypothesised score at 5 percent
     level of significance.
6.  a) What is a simple linear regression ?
     b) Explain the managerial uses of correlation analysis.
     c) Data given below indicate the ranks given between branches of a nationalised
         bank on the basis of their deposit mobilisation and recovery of loans. Calculate
        the coefficient of correlation between the deposit mobilisation and recovery of
       loans.

Deposit                    1   2    3   4     5      6     7    8      9    10   11     12   13   14      15  
Mobilisation

Loan                        4    2    9   1    7      10    8    13    5    3     11      6     12   15    14  
Recovery

7.  a)  What is sample space ?
     b)  Explain the condition of poisson distribution.
     c)  Normally distributed average price per ton of rice is Rs.3,500 with a standard
        deviation of Rs. 100. Calculate the probability that the price will lie between
        Rs.3,400 and Rs. 3,600.
8.  a)  What is median ?
     b)  Explain the relevance of median in business decision.
     c) Find the median for the following distribution :
Gross Profit as a             0-10                    10-20              20-30         30-40       40-50
Percentage of Sales 

Number of                        22                        38                   46                35            20
Companies 
9.  a) Define matrix.
     b) Explain inverse of a matrices.
     c) Describe any five types of matrices.
10. a)  What is integration ?
      b)  Explain the business applications of differentiation and integration.
     c)   Differentiate y =x2 from first principles.