Part - 1:
A survey was conducted among the residents of Pune City, its suburbs and the Pune Cantonment area. The following three pie diagrams show their respective preferences for living in City, Suburb and cantonment.
Questions:
1. Do you see similar preference distribution in the three groups of residents?
2. Which residents are most happy about where they are actually living?
3. Which residents are the least happy about where they are actually living?
2. Description
Suppose you are doing market research for a company that sells automotive accessories. You are interested in the types of cars driven by customers of a particular mall. On one particular day, you count the following types of cars in the lot:
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Family car Economy car Economy car Utility van
Family car Wagon Wagon Wagon
Sports car Economy car Utility van Family car
Pickup truck Utility van Sports car Utility van
Wagon Wagon Wagon Family car
Pickup truck Utility van Sports car Utility van
Economy car Economy car Utility van Sports car
Utility van Sports car
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Questions:
1. Prepare appropriate frequency distribution
2. Represent above data by suitable graph
3. Description:
In a series of four one day cricket matches, Sachin and Sourav Scored as follows:
Sachin: 99 116 95 110
Sourav: 110 145* 40 20
* : not out
Question: If you have to select the ‘Man of the Series' out of these two only whom will you select? Why?
4. Description
Following are the data on height of father (X) and height of son (Y)
|
X (in cms)
|
165
|
166
|
167
|
167
|
168
|
169
|
170
|
172
|
|
Y (in cms)
|
167
|
168
|
165
|
168
|
172
|
172
|
169
|
171
|
Questions
(a) Plot these data and comment on the nature of relationship between the two variables under consideration.
(b) Find correlation between (X, Y).
5. Using the data in Q. 4 above, find regression equation of height of son on father's height.
Part - 2:
A financial record of two companies A and B are examined to determine whether each company showed a profit (P) or not (N) during the last financial year.
Question: (a) Is this a random experiment? Justify your answer.
(b) List the simple events associated with this experiment.
(c) Suppose P(A shows profit) = 0.8 and P(B shows profit) = 0.2, what is the probability that either of the company shows profit.? (State assumptions).
2. Description
In the following Venn diagram the ten sample points shown are equally likely.
Question: State following probabilities:
1. P(A), P(B), P( )
2. Are A and B mutually exclusive and exhaustive? Justify your answer.
Case 3: Description
Study the following diagrams and answer the questions
Following are the marks awarded to 8 competitors by two judges during a music competition.
|
Participant No.
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
Judge 1
|
75
|
78
|
83
|
56
|
89
|
90
|
65
|
95
|
|
Judge 2
|
72
|
80
|
83
|
60
|
92
|
94
|
70
|
93
|
Question: Can you say that two judges agree with each other.
Case 4: Description
A person visits a family having three children. He notices that one male child was playing with toys.
Question :
(a) State the sample space of this experiment.
(b) What is the probability the family has all children of the same sexes?
(c) What is the probability that family has children of both the sexes?.
Case 5: Description
It is hypothesized that average performance of female students is better than male students in the subject of Mathematics of HSC examination. To test the claim a student randomly selects 8 male and 8 female students from his class and records the marks in Mathematics. Following are the marks in Mathematics of selected students:
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Student No: 1 2 3 4 5 6 7 8
Male student 65 72 61 56 76 81 63 85
Female student 85 81 76 61 72 56 63 100
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Question
(a) Suggest appropriate statistical analysis of the above data.
(b) Can you apply any test to check the claim? Give in brief the details of the test and perform it on the above data and conclude.