IMT – 24: QUANTITATIVE TECHNIQUESMT2
PART – A
Q1. What do you mean by Quantitative Techniques? What are different forms of Quantitative Techniques? Explain the importance of Quantitative Techniques in business.
Q2. What are the different statistical tools used for organizing data. The following frequency distribution represents the number of days during a year that the faculty of the college was absent from work due to illness.
Number of Days

Number of Employees

02

5

35

10

68

20

911

10

1214

5


Total 50

(a) Construct a frequency distribution for this data.
(b) Construct a greater than cumulative frequency distribution as well as a less than cumulative frequency distribution for this data.
(c) How many employees were absent for less than 3 days during the year?
(d) How many employees were absent for more than 8 days during the year?
(e) Draw the cumulative frequency ogives (greater than and less than) .What is the significance of intersection of these two ogives?
Q3. What are different uses or functions of statistics? How do you think each function might be used to solve Business problems?
Q4(a) Explain the use of different measures of central tendency in description of data. Suppose you are given output of a factory for 5 years & you are asked to work out the average rate of growth of this output, what measures of central tendency you will use.
(b) Paul the plumber sells five types of drain cleaner each type, along with the profit per can & the no. of cans sold, is shown in the table. Calculate the average profit of plumber
Cleaner

Profit per Can (x)

Sales value in can (w)

Xw

Main Drain

Rs 6.00

15

Rs 90.0

Glunk out

Rs 2.00

3

Rs 6.00

Bubble up

Rs 3.50

7

Rs 24.50

Dream Drain

Rs 5.00

15

Rs 75.00

Clear more

Rs 7.50

12

Rs 90.00

Total

Rs 24.00

52

Rs 285.50

5(a) What do measures of dispersion and skewness indicate? Explain the use of standard deviation in Business.
(b) Do you think Absolute measure of standard deviation is always useful in business? If not, explain the use of alternate measures of Dispersion.
(c) Two workers on the same job shown the following results over a long period of time.
A B
Mean time of completing the job (in minutes) 40 30
S.D. (in minutes) 8 5
(i) Which worker appears to be more consistent in the time he requires to complete the job?
(ii) Which worker appears to be faster in completing the job?
PART – B
1. A recent court case in Madison Country, Kentucky, centered on the hiring practices of the local telephone company. The company planned to hire 3 new employees. There were 8 applicants for the jobs, 6 of whom were men. All 3 of those hired were men. A charge of sex discrimination was levied against the company. How would you decide?
2. Only 60 percent of the students in Professor Harmond’s statistics class pass the first test. Of those who pass, 80 percent studied; 20 percent of those who didn’t pass studied. Should you study for his tests?
3. The probability that John can solve a particular statistics problem is 40 percent. There is a 70 percent chance that Fred can solve it. What is the probability it is solved? Assume that John and Fred work separately and the outcomes are therefore independent.
4. What do you mean by

Expected Value and

Variance of a discrete random variable?

The number of houses sold each month by Ponder Real Estate, which has varied from 5 to 20, is reported, along with the frequency of each sales level, in the first two columns of the table shown below.
Number of Months

Houses (X_{i})

P (X_{i})

3

5

3 / 24 = 0.125

7

8

7 / 24 = 0.292

4

10

4 / 24 = 0.167

5

12

5 / 24 = 0.208

3

17

3 / 24 = 0.125

2

20

2 / 24 = 0.083

Mr. Ponder hopes these numbers reflect an increase in the average number of sales over the 7.3 he sold in earlier months and a reduction in the variability of monthly sales that had been σ = 5.7. If not, he has decided to sell the business and become a rodeo clown. What advice can you offer Mr. Ponder?
Q5. A state commission has been formed to reduce response times of local fire departments. A group of experts is attempting to identify those city fire departments whose response time is either in the lowest 10 percent, or who take longer than 90 percent of all fire departments in the study. Those in the first group are to serve as models for the less efficient fire units in the second group.
Data show that the mean response times for a certain class of fire departments is 12.8 minutes, with a standard deviation of 3.7 minutes.
PART – C
1. Define Regression Analysis.
(a) Explain its use in Business.
(b) Distinguish between
(i) Simple regression & multiple regression.
(ii) Deterministic and Probabilistic model.
(c) As a furniture retailer in a certain locality, you are interested in finding the relationship that might exist between the number of building permits issued in that locality in past years and the volume of your sales in those years. You accordingly collected the data for your sales (Y, in thousands of rupees) and the number of building permits issued (X, in hundreds) in the past 10 years. The result worked out as:
n = 10, ΣX = 200, ΣY = 2200
ΣX2 = 4600, ΣXY = 45800, ΣY2 = 490400
Answer the following:
(i) Calculate the coefficients of the regression equation.
(ii) It is expected that there will be approximately 2000 building permits to be issued next year. On this basis, what level of sales can you expect next year?
(iii) On the basis of the relationship you found in (i) one would expect what change in sales with an increase of 100 building permits?
(iv) State your estimate of (ii) in the (iii) so that the level of confidence you place in it is 0.90.
2. Explain the concept of standard error of estimate and the coefficient of determination. How can the coefficient of determination be used as a goodness of fit? If the value of the coefficient of correlation is 0.9 does this indicate that 90% of the variation in dependent variable has been explained by variation in the independent variable? If not, give reasons.
3(a) What do you mean by Time – series? What are different components of a Time series? Explain the object of smoothing and the techniques used for smoothing.
(b) Shown here are shipments (in millions of dollars) for electric lighting and wiring equipment over a 12 month period. Use these data to compute
(i) 4month moving average for all available months.
(ii) Give the error of forecast.
Months

Shipments

January

1,056

February

1,345

March

1,381

April

1,191

May

1,259

June

1,361

July

1,110

August

1,334

September

1,416

October

1,282

November

1,341

December

1,382

4(a) Distinguish between
(i) Population and Sample
(ii) Parameter and Statistic
(b) Why is sampling necessary in statistical investigation? Explain the important methods of sampling commonly used.
5(i) What are the steps to a hypothesis test?
(ii) Distinguish between a type I error and type II error.
(iii) The labor agreement between the United Auto Workers (UAW) and Ford Motor Company (FMC) required that the mean output for a particular production section be held at 112 units per month per employee. Disagreement arose between UAW and FMC as to whether this standard was being maintained. The labor agreement specified that if mean production levels dropped below the stipulated amount of μ = 112, FMC was permitted to take “remedial action.” Due to the cost involve, only 20 workers were tested, yielding a mean of 102 units. Assume that a standard deviation of 8.5 units was found and that output levels are normally distributed. Does a 90 percent confidence interval tend to suggest a violation of the labor contract, thereby allowing the remedial action?
CASE STUDY – I
Suppose the director of the Delhi Govt Sanitation Department is interested in the relationship between the age of a garbage truck and the annual repair expense she should expect to incur. In order to determine this relationship, the director has accumulated information concerning four of the trucks the city currently owns (Table 1).
Table 1

Truck Number

Age of Truck in Years (X)

Repair Expense During Last Year in Hundreds of $ (Y)



Annual TruckRepair Expenses

101

5

7


102

3

7


103

3

6


104

1

4


Questions:
With the information in Table 1
(a) Find the numerical constants a and b for the regression line.
(b) Determine the equation of the regression line and describe the relationship between the age of a truck & its annual repair expense with the help of Regression Line?
(c) What would be the annual repair expense for the truck that is 4 years old?
(d) Compute the residuals to test whether this line is a good fit.
CASE STUDY – II
You collected data from 500 economists in academe, private industry, and government concerning their opinions on whether the economy would prove stable, would expand, or would enter a period of contraction in the near future. However, part of the information was lost, resulting in the partial contingency table seen below. Based on the remaining data, create a probability table.
Economy

Economists

Stable

Expansion

Contraction

Total

Academe

125


100


Private Industry


35


110

Government

25

40


65

Total

200




Questions:
a. Find P(S /A)., P(G), P(A), P(AΩE)