ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Mathematics Statistics)
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1.
2.
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Course: Statistics-II (395)
Level: Intermediate
Semester: Autumn, 2015
Total Marks: 100
Pass Marks: 40
ASSIGNMENT No. 1
Q.1 a)
b)
Q.2 a)
b)
What is the importance of normal distribution in statistical theory? Describe
its properties.
The lengths of rods produce in a workshop follow a normal distribution with
mean  and variance 4. If 10% of the rods are less than 17.4 cm long. Find
the probability that a rod chosen at random will be between 18 and 23 cm
long.
(10+10)
What is meant by the sampling distribution of sample proportion? Describe
the properties of the sampling distribution of sample proportion.
A finite population consists of five values 2, 4, 6, 8 and 10. Take all possible
samples of size 2 which can be drawn with replacement from this population.
Assuming the 25 possible samples equally likely, construct the sampling
distributions of sample means and sample variances and find the mean of
these distributions. Calculate the mean and variance of the population and
verify that:
(10+10)
i)
Q.3 a)
b)
Q.4 a)
ii.
Define Student’s t-statistics. What assumptions are made about the
population where the t-distribution is used?
The contents of 10 similar containers of a commercial soap are: 10.2, 9.7,
10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3 and 9.8 litres. Find 99% confidence
interval for the mean soap content of all such containers, assuming an
approximate normal distribution.
(10+10)
A random sample of 16 values from a normal population showed a mean of
41.5 inches and a sum of squares of deviations from this mean equal to 135
1
b)
Q.5 a)
b)
(inches)2. Show that the 95% confidence limits for this mean are 39.9 and
43.1 inches.
In a random sample of 400 adults and 600 teenagers who watched a certain
television programme. 100 adults and 300 teenagers indicated that they
liked it. Construct 95% and 99% confidence limits for the difference in
proportions of all adults and all teenagers who watched the programme and
liked it.
(10+10)
Outline the fundamental procedure followed in testing a null hypothesis.
A sample of 400 male students is found to have a mean height of 67.47
inches. Can it be regarded as a simple random sample from a
large population with mean height 67.39 with standard deviation of 1.3
inches?
(10+10)
ASSIGNMENT No. 2
Q.1 a)
b)
Q.2 a)
b)
A group of 12 students are found to have the following I.Q.’s:
112, 109, 125, 113, 116, 131, 112, 123, 108, 113, 132, 128
Is it reasonable to assume that these students have come from a large
population whose mean I.Q.’s is 115?
Another group of 10 students are found to have the following I.Q.’s:
117, 110, 106, 109, 116, 119, 107, 106, 105, 108
Can we conclude that both the groups of students have come from the same
population?
In a population that has certain minor blood disorder, samples of 100 males
and 100 females are taken. It is found that 31 males and 24 females have the
blood disorder. Can we conclude at 0.01 level of significance that proportion
of men who have blood disorder is greater than proportion of women? (10+10)
Explain what is meant by:
i)
regression
ii)
regress and
iii) regressor
Determine the regression line and estimate the weight of a student whose
height is 68 inches:
Height (inches) xi
Weight (pound) yi
72
178
66
141
67
158
69
165
74
180
61
133
66
159
62
140
70
160
63
136
Find also the estimated values for given values of height. Show that the sum of
the estimated values is equal to the sum of the observed values of weight. Find
the deviations ei = yi – ŷi. Show that these deviations add to zero.
(10+10)
2
Q.3 a)
b)
Differentiate between regression and correlation problems by giving
examples.
Given that means and variances of two series X and Y are:
Mean:
Variance:
X-series
25
25
Y-series
38
36
The correlation coefficient between X and Y is 0.75. Estimate the most
plausible value of Y for x=40 and most plausible value of X for y=58. (10+10)
Q.4 a)
b)
Q.5 a)
b)
Describe the following terms:
i)
Secular trend
ii)
Seasonal variations
iii) Cyclical fluctuations
iv) Irregular movements
The parabolic trend equation for the projects of a company (in thousand
rupees) is ŷ = 10.4 + 0.6x + 07x2, with origin at 1980 and unit of
measurement for x is one year. Shift the origin to 1975.
(10+10)
How are computers generally classified? What are the four major categories
of computers? Also explain the working of Arithmetic Logical Unit (ALU).
What is Binary Number System? What is it used in computer?
(10+10)
3