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Transcript
```ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Statistics)
WARNING
1.
2.
PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING
THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD
OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.
SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.
Course: Statistics & Probability (3447)
Total Marks: 100
Semester: Autumn, 2016
Pass Marks: 50
ASSIGNMENT No. 1
Note: All questions carry equal marks.
Q.1 a)
b)
Q.2 a)
b)
What is a statistical data? Distinguish the following:
(10)
i) Primary and secondary data
ii) Qualitative and quantitative data
iii) Discrete and continuous data
Arrange the data given below in an array and construct a frequency
distribution, using a class interval of 5.00. Indicate the class limits and class
boundaries clearly.
(10)
79.4, 71.6, 95.5, 73.0, 72.2, 81.8, 90.6, 55.9, 75.2, 81.9, 68.9, 74.2, 80.7,
65.7, 67.6, 82.9, 88.1, 77.8, 69.4, 83.2, 82.7, 73.8, 64.2, 63.9, 58.3, 48.6,
83.5, 70.8, 72.1, 71.6, 59.4, 77.6.
Describe the properties of standard deviation. Explain standard coefficient of
dispersion.
(10)
The following frequency distribution shows the marks in a test of 100
students.
(10)
Marks
Number of students
30–39
10
40–49
14
50–59
26
60–69
20
70–79
18
80–89
12
Calculate the mean, median, mode and standard deviation. Also interpret the
results.
Q.3 a)
Explain what is meant by random experiment? Define sample space, random
event, complementary events, equally likely events and exhaustive events. (10)
1
b)
A marble is drawn from a box containing 10 red, 15 black, 5 green and 10
yellow marbles. Find the probability that the marble is (i) black (ii) not green
or yellow (iii) red or black or green (iv) not blue.
(10)
Q.4 a)
What is meant by (i) binomial experiments (ii) binomial random variable and
binomial probability mass function?
(10)
The incidence of occupational disease in an industry is such that the
workmen have a 20% chance of suffering from it? What is the probability
that out of 6 workmen, (i) not more than 2 (ii) 4 or more will catch the
disease.
(10)
b)
Q.5 a)
b)
Differentiate between parameter and statistics. Explain the advantages of
sampling.
(10)
Draw all possible samples of size 2 without replacement from a population
consisting of 4, 7, 8, 12, and 18. From the sample distribution of sample
means and verify the results.
(10)
ASSIGNMENT No. 2
Total Marks: 100
Pass Marks: 50
Note: All questions carry equal marks.
Q.1 a)
b)
Q.2 a)
b)
Explain in detail the procedure of testing a null hypothesis with suitable
example.
(10)
For a sample of 60 women taken from a population of over 5,000 enrolled in
a weight-reducing program a nationwide chain of health spas, the sample
mean diastolic blood pressure is 101 and the sample standard deviation is 42.
At a significance level of 0.02 on the average, did the women enrolled in the
program have diastolic blood pressure that exceeds the value of 75?
(10)
Explain with examples the difference between:
(10)
i)
Simple Hypothesis and Composite Hypothesis
ii)
Acceptance Region and Rejection Region
iii) Statistic and Test Statistic
iv) Type-I Error and Type-II Error
Consider the case of pharmaceutical manufacturing company testing two
now compound indenting to reduce bold pressure levels. The compound is
administered to two different sets of laboratory animals. Group one, 71 of
100 animals testing respond to drug one with lower bold pressure levels. In
group two 50 of 90 animals testing respond to drugs two lower blood
pressure level the company want to test at the 5% level whether there is a
2
different between the efficacies of these two drugs. How should proceed
these drugs.
(10)
Q.3 a)
b)
Define and explain the terms regression and correlation. Describe the
properties of least square regression line.
(10)
The following sample of 8 grade point averages and marks in matriculation
was observed for students from a college.
(10)
Score
GPA
480
2.7
490
2.9
510
3.3
510
2.9
530
3.1
550
3.0
610
3.2
640
3.7
Fit Y = a + βX + ε by least squares method and estimate the mean GPA of
students scoring 600 marks.
Q.4 a)
b)
What is meant by a random variable? Differentiate between the discrete
random variable and continuous random variable.
(10)
At the 0.10 level of significance, can we concluded that the following 400
observations follow a Poisson distribution with λ = 3?
(10)
0
20
Number of arrivals per hour
Number of hours
Q.5 a)
b)
1
57
2
98
3
85
4
78
5 or more
62
What is meant by analysis of variance? Explain the general procedure
for it.
(10)
Three training methods were compared to see whether they led to greater
productivity after training. The following are the productivity measures for
individual trained by each method.
(10)
Method 1
Method 2
Method 3
45
59
41
40
43
37
50
47
43
39
51
40
53
39
52
44
49
37
At the 0.05 level of significance, do the three training methods lead to
different levels of productivity?
3
```