1
Seat No.: Enrolment No.:
GUJARAT TECHNOLOGICAL UNIVERSITY
BPLAN SEMESTER II- • EXAMINATION WINTER 2016
Subject Code: 1025504 Date: 21/11/2016
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.
Q.1 A random sample of 34,562 athletes is taken across India. Sample mean age
of them quitting the sports is found out to be 29 years. For estimating the
claim that mean age of quitting the sports is less than 29 years, what will be
your null hypothesis for hypothesis testing
06
H0 29 H0 29
H0 H0 29
What does sample correlation coefficient r denotes when it is closer to 0
Strong negative linear
relationship
Strong positive linear
relationship
Weak liner relationship None of the above
In simple linear regression model, b0 denotes
Regression slope Dependent variable
Regression intercept Independent variable
For a data set with degree of freedom 12 and confidence level of chi
square critical value would be
24.725 31.264
26.217 32.910
Decision making analysis is a method for
Reducing uncertainty Getting perfect information
Increasing uncertainty None of the above
Incorrect rejection of a true null hypothesis is
Type II error Not an error
Type I error Type III error
2

Define following terms: (Any Two)
Type II error
Sum of square of regression
Expected value of perfect information
Coefficient of determination
04
Q.2 A soft drink manufacturing company states on the product label that all its bottles
contains 300 ml. of soft drink. A sample of 1200 bottles is tested and sample
mean of 294 ml. is derived. Considering the population standard deviation to be
45, estimate weather all bottles contain 300 ml. of soft drink or not.
05
Explain in detail, Type I and Type II errors in reference of hypothesis testing 05
OR
A random sample of 15 enthusiasts was carried out in Parimal garden. Below
mentioned is their calorie intake in (kcal) in food per day.
1.8 1.5 1.7 2.2 2.4 1.6 1.5 2.1 2.2 2.0 1.9 1.9 1.4 1.7 1.6
Assuming that the sample came from an underlying normal distribution,
investigate the claim that their mean calorie intake exceeds 1.7 kcal day.
05
Q.3

For working out electricity requirements in MBSIR, electricity requirements of 5
cities are studied and they are as per below
Population of City (Lakhs) Electricity
18 120
20 185
22 180
36 275
42 280
For the given data set
Find values of all y caps and draw a regression line model diagram
05

24
Estimate
Electricity requirement for a population of 35,00,000
Optimum population size for electricity consumption of 150 KW
05
OR
3
Q.3

Find out SST, SSR and SSE
05
What is coefficient of determination 05
Q.4

x y
24 43
32 65
16 54
17 23
19 45
For the given data set
Find the value of r
05
Plot a regression line diagram 05
OR
Q.4

A real estate developer is planning to develop a township on a piece of land. The
investment requirement for the project is around 18 crores and if the project gets
completely sold out then he will generate profit of Rs. 45 crores. However
looking at the current scenario, there are only 25% chances that the project will
get sold out completely, so under that situation he will have to incur losses of Rs.
12 crores.
He has also got an offer to sell of the land and in that scenario; he will out rightly
make a profit of Rs. 22 crores.
For the above given situation
What decision should the developer take under
Maximax criterion
Maximin criterion
Maximum likelihood criterion
Even state of probabilities
Given state of probabilities
05
What is the maximum amount that he should invest in hiring a market
specialist?
Prepare a decision tree for even and given state of probabilities
05
4
Q.5

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 22 16
Mumbai 14 15 24
Chennai 16 21 18
Kolkata 18 15 18
Bhopal 27 21 8
Find out critical value for chi-square analysis for the above given data for
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
Q.5


220 180 150 130 210
190 310 350 280 270
250 160 140 330 290
Above data shows ticket prices of various multiplexes in the city over weekend.
It is known that standard deviation in the prices over peak demand is 30.
Estimate the mean price of ticket with 95% confidence
How many samples would be required, if we need the estimate range to be
between 5 rs. on either side at confidence level of 99%
05
05
5
6