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IMT 24 Quantitative Techniques M1

PART– A

1. What do you mean by Quantitative Techniques? What are different forms of Quantitative Techniques?

Explain the importance of Quantitative Techniques in business.

2. 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

0-2 5

3-5 10

6-8 20

9-11 10

12-14 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?

3. What are different uses or functions of statistics? How do you think each function might be used to solve

Business problems?

4(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 Quantitative Technique. ……………………………………. Page 3 of 6 ……………………………………………………………………. IMT-24

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

a. Expected Value and

b. Variance of a discrete random variable?

c. 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.

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 Quantitative Technique.

Number of Months Houses (Xi

) P(Xi

)

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?

5. 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, ∑X = 200, ∑Y = 2200

∑X

2

= 4600, ∑XY = 45800, ∑Y

2

= 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 co-efficient of determination. How can the coefficient of determination be used as a goodness of fit? If the value of the co-efficient 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) 4-month moving average for all available months.

(ii) Give the error of forecast. Quantitative Technique.

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).

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.

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

Table 1 Truck Number Age of Truck in

Years (X)

Repair Expense During Last Year in

Hundreds of $ (Y)

Annual Truck- Repair

Expenses

101 5 7

102 3 7

103 3 6

104 1 4

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.

Questions:

a. Find P(S /A)., P(G), P(A), P(AΩE)

Economy

Economists Stable Expansion Contraction Total

Academe

Private Industry

Government

Total

125

25

200

35

40

100

110

65

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