Seat No.: Enrolment No.:
GUJARAT TECHNOLOGICAL UNIVERSITY
B.PLAN SEMESTER II EXAMINATION WINTER 2018
Subject Code: 1025504 Date: 07/01/2019
Subject Name: Statistical and Quantitative Methods in Planning II
Time: 02:30 PM to 04:30 PM Total Marks: 50
Instructions:-
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Use appropriate examples and illustrations where necessary.
Q.1.

Fill in the blanks (any five)
05
I.
Data before it is arranged and analyzed is called
II.
Cluster sampling is type of sampling.
III.
If sample size is <30 then it follows distribution.
IV.
Interquartile range divides the whole data set in to equal parts.
V.
Full form of ANOVA
VI.
The χ2 test is also known as

Define the following term:
05
I.
Slack variable
II.
Coefficient of determination
III.
Linear programming
IV.
Type II error
V.
Expected value of perfect information
Q.2.

A chips manufacturing company states on the product label that all its packages contains 250 gms. of wafers. A sample of 1500 packages is tested and sample mean of 247 gms. is derived. Considering the population standard deviation to be 60, estimate weather all packages contain 250 gms. of chips or not.
05

Explain in detail, Type I and Type II errors in reference of hypothesis testing.
05
OR

A construction company owns four cars. Develop the regression model to estimate annual maintenance expenditure from the following data.
Age of Car (Year)
16
8
6
2
Annual maintenance
20
15
13
9
Calculate the coefficient of correlation and determination. Estimate the annual maintenance expenditure for 10 years.
05
Q.3.

Write short note on:
Quantitative and qualitative data.
ii) What measures and parameters should be considered while preparing the survey questioner for slum survey?
05

1991
1992
1993
1994
1995
1996
12500
13250
14300
15750
17600
18440
Calculate the average percentage increase of population over a given time period, and use this to estimate the population of 2004.
05
OR

Write short note on ANOVA and explain One way and Two way ANOVA.
05

Formulate the linear programming by simplex method for Maximization of 12X1+3X2+X3 subjected to
10X1+2X2+X3≤100
7X1+3X2+2X3≤77
2X1+4X2+X3≤80
05
Q.4.
A survey has been conducted in four major cities to identify the professional interest of young students:
Name of state/ career option
Medical
Engineering
Management
Delhi
20
20
10
Mumbai
15
15
20
Chennai
10
20
20
Kolkata
18
20
12
Bhopal
22
20
8

Find out critical value for chi-square analysis for the above given data from confidence level of 97.5% and 99.99%.
05

Is there a relation between the student opting for professional career and region he belongs to?
05
OR

Write short note:
Explain: Cyclic Variation, Irregular Variation(With example)
05

A person wants to know the average monthly income for the person residing in Surat city, which is divided in to five Zones. Zone wise data of population and income is as given below. Calculate the average annual personal income for city.
Zone
Average monthly income
Population
A
21000
500
B
16500
750
C
12000
1100
D
18000
600
E
17250
725
05
Q.5.
For a given farm land of 200 acres, what amount of wheat and cotton should be grown to earn maximum profit?
The farmer makes a profit of Rs. 300/ acre from wheat and Rs. 200/ acre from cotton, however wheat takes 3 hrs acre of labour to harvest and cotton takes 1 hr acre to harvest. He only has a total of 300 hours of labour.

List down the decision variables, objective function and constrains for the above given situation and with the help of graphical method solve the above given situation.
05

Will there be change in the situation if the area under cotton is restricted to maximum of 20 acres? If yes, provide the maximum profit earning break up for this situation.
05
OR

Explain using Sketches: Kurtosis, Skewness, interfractile range.
05

What is Hypothesis? In which conditions "Null Hypothesis" is proved?
05