Final: 15-2-2017
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 ASSIGNMENT(S) BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.
Course: Statistics for Management (5412)
Level: Associate Degree in Commerce
Semester: Spring, 2017
Total Marks: 100
Pass Marks: 50
ASSIGNMENT No. 1
Q. 1 (a)
(b)
Define Descriptive and Inferential Statistics. Write a short note on arranging
data using the data array and the frequency distribution.
(10)
Find mean, median, mode, lower quartile (Q1) and upper quartile (Q3) from
the following data:
(10)
Class Interval
1-5 5-10 10-15 15-20 20-25 25-30 30-35
Frequency
3
10
24
30
25
8
4
Q. 2 (a)
(b)
Explain the difference between absolute measure and relative measure. (10)
Draw a Histogram giving the steps involved for the following frequency
distribution:
(10)
Mid values (x)
30
35
40
45
50
55
60
65
Frequency (f)
5
19
25
45
52
30
12
5
Q. 3 (a)
What is meant by measures of central tendency? Explain various methods of
finding Central tendency.
(10)
Find Arithmetic Mean, Median, Mode, Standard Deviation and Variation for
the following data:
(10)
Class
3.7-4.1 4.2-4.6 4.7-5.1 5.2-5.6 5.7-6.1 6.2-6.6
Frequency
9
12
8
15
4
3
(b)
Q. 4 (a)
(b)
(c)
Q. 5 (a)
(b)
Explain what is meant by i) Statistical hypothesis ii) Test-statistic
iii) Significance Level
(10)
The masses in grams, of thirteen ball bearings taken at random from a batch
are 21.4, 23.1, 25.9, 24.7, 23.4, 21.5, 25.0, 22.5, 26.9, 26.4, 25.8, 23.2 and
21.9. Calculate a 95% confidence interval for the mean mass of the
population, supposed normal, from which these masses are drawn.
(05)
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. (05)
What is difference between a one-sided and a two-sided test? When should
each be used?
(10)
A random sample of 100 workers with children in day care shows a mean
day-care cost of Rs. 2,600 and a standard deviation of Rs. 500. Verify the
department’s claim that the mean exceeds Rs. 2,500 at the 0.05 level with
this information.
(10)
ASSIGNMENT No. 2
Q. 1 (a)
(b)
Q. 2 (a)
(b)
Q. 3 (a)
(b)
Explain how the null hypothesis and the alternative hypothesis are
formulated? Write down all the steps involved in testing of hypothesis. (10)
A random sample of 16 values from a normal population gave a mean of 42
inches and a sum of squared deviations from this mean as 135 (inches) 2. Test
the hypothesis that the mean in the population is 43.5 inches.
Another random sample of 9 values from another normal population gave
a mean of 41.5 inches and a sum of squares of deviations from this mean is
128 (inches)2. Test the hypothesis that mean of first population equals the
mean of the second population, assuming that the variances of the two
populations are equal.
(10)
Means of random samples, each of size 10, from two normal populations
with the same standard deviation were found to be 16 and 20 respectively,
Further; the sample standard deviations were equal to 5 and 7 respectively.
Test the hypothesis that the populations have the same mean, using 0.05 level
of significance.
(10)
The test was given to a group of 100 scouts and to a group of 144 guides.
The mean score for the scouts was 27.53 and the mean score for the guides
was 26.81. Assuming a common population standard deviation of 3.48, test,
using a 5% level of significance, whether the scouts performance in the test
was better than that of the guides.
(10)
Differentiate between regression and correlation problems, giving examples. (10)
Fifteen boys took two examination papers in the same subject and their
marks as percentages were as follows, where each boy’s marks are in the
same column.
Paper I xi
Paper II yi
Q. 4 (a)
(b)
Q. 5 (a)
65
78
73
88
42
60
52
73
84
92
60
77
70
84
79
89
60
70
83
89
57
73
77
88
54
70
66
85
89
89
Calculate the equation of the line of regression of Y on X.
(10)
What is a scatter diagram? Describe its role in the theory of regression?
The following are the measurements of height and weight of 8 men:
Height (inches) xi
78
89
97
69
59
79
68
Weight (pound) yi
125 137 156 112 107 136 123
Calculate the correlation coefficient between the height and weight.
(10)
61
104
(10)
Construct the simple index numbers from the following data taking i) 1990
as base year ii) average of first three years as base iii) average of all years as
base.
(10)
Years
Prices
(b)
Total Marks: 100
Pass Marks: 50
1990
20
1991
18
1992
23
1993
24
1994
25
1995
27
1996
28
1997
30
1998
32
1999
33
The prices and quantities of three items are given below. Using 2015 as base
period, compute Laspeyre’s Index, Paasche’s Index and Fisher’s Ideal Index
Numbers.
(10)
Prices
Quantities
Year
2015
2016
2015
2016
Books
45
50
5
6
Copies
55
70
6
7
Pens
12
18
12
13
____[ ]____