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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
BPLAN SEMESTER • EXAMINATION SUMMER 2017
Subject Code: 1025504 Date: 30/05/2017
Subject Name: Statistical and Quantitative Methods in Planning II
Time: 10.30AM to 12.30PM 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 1,50,000 infants is taken across Ahmedabad. Sample mean age for them to start walking is found out to be 11 months. For estimating the claim that mean age of an infant starting to walk is less than 11 months, what will be your null hypothesis for hypothesis testing
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H0 11
H0 11
H0
H0 11
Sample coefficient correlation is used to measure
Cause
Strength
Both
None
Y bar represents
Average value of dependent variable
Observed value of dependent variable
Estimated value of y for given value of x
None of the above
For a data set with degree of freedom 11 and confidence level of chi square critical value would be
31.264
29.588
17.275
24.725
Maximin criterion under decision making analysis is a decision under
Certainty
Uncertainty
Risk
Normal condition
Coefficient of determination square' is directly proportional to
Total sum of squares
Regression of sum of squares
Sum of squares of error
None of the above
2

Define following terms: (Any Two)
Sum of square of errors
Regression intercept
Null hypothesis
04
Q.2

A soft drink manufacturing company states on the product label that all its packages contains 300 ml. of soft drink. A sample of 2540 packages is tested and sample mean of 293 ml. is derived. Considering the population standard deviation to be 90, estimate weather all bottles contain 300. ml of soft drink or not.
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Explain in detail, the process of hypothesis testing
05
OR

A random sample of 9 students was carried out in a class room. Below mentioned are their marks in mathematics out of 100.
45 80 56 62 36 51 47 76 53
Assuming that the sample came from an underlying normal distribution, investigate the claim that its mean exceeds 50%.
05
Q.3

For working out electricity requirement in Amravati, electric consumption of 5 cities are studied and they are as per below
Population of City (Lakhs)
Electricity consumption (Billion KW)
45
70
10
20
25
35
12
25
30
45
For the given data set
Draw a regression line model diagram
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Estimate
Electricity requirement (Billion KW) for a population of 37,00,000
Optimum population size for Electricity requirement (Billion KW) of 100 (Billion KW)
05
OR
3
Q.3

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

x
y
25
7
12
4
18
12
15
9
6
11
For the given data set
Find the value of r
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Plot a regression line diagram
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OR
Q.4

An individual is informed about presence of oil beneath his land. The investment requirement for digging up the land is around 12 crores and if he finds oil then he will generate profit of Rs. 180 crores. However, there are only 15% chances that there will be oil, so under that situation he will have to incur losses of Rs. 20 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. 50 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
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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
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Q.5

A survey has been conducted in different classes in a school to identify favorite subject of students
Standard
Mathematics
Science
Social studies
6th
12
18
20
7th
15
20
15
8th
30
10
10
9th
25
12
13
10th
30
15
5
Find out critical value for chi-square analysis for the above given data for confidence level of 97.5% and 99.99%
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Is there a relation between the standard of student and favorite subject
05
OR
Q.5

Explain in detail SSE,SSR and SST with the help of a diagram
05

What is estimation? What are major differences between point estimator and interval estimator?
05
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