ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Mathematics and Statistics)
1. 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.
2. SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN “AIOU PLAGIARISM POLICY”.
Course: Statistics–II (395) Semester: Spring, 2013
Level: F. Sc Total Marks: 100
ASSIGNMENT No. 1
Q. 1 (a) Define and explain estimate, estimator and properties of a normal distribution. (10)
(b) Normal distribution is symmetric with a single peak. Does this mean that all symmetric distribution are normal? Explain. (05)
(c) In a normal distribution 
. Find third and fourth moment about mean. (05)
. Find third and fourth moment about mean. (05)
Q. 2 (a) What is bias? Define sampling error. How it can be reduced? (05)
(b) What is difference between precision and accuracy? (05)
(c) A small professional society has N = 4500 members. The president has mailed n = 400 questionnaires to a random sample of members asking whether they wish to affiliate with a large group. Assuming that the proportion of the entire membership favoring consolidation is 
. Find the mean and standard error of the sample proportion. (10)
. Find the mean and standard error of the sample proportion. (10)
Q. 3 (a) A family has 5 children; the sex of child is given below: (10)
Child
|
1
|
2
|
3
|
4
|
5
|
Sex
|
B
|
G
|
G
|
B
|
B
|
(i) Find the proportion of boys in the population.
(ii) Select all possible samples of size 3 without replacement. Make the sampling distributions of boys in the samples and verify that: 
ii) 
(b) A population consists of four numbers 3, 7, 9 and 11. Take all possible samples of size 2 with replacement form this population. Find the mean and unbiased variance for each sample. Also calculate the mean and variance of the population. (10)
Q. 4 (a) Calculate 95% confidence interval for population mean when a random sample selected from the population gave the values: (10)
23
|
27
|
30
|
31
|
33
|
33
|
35
|
36
|
40
|
41
|
42
|
44
|
46
|
47
|
47
|
48
|
49
|
50
|
51
|
53
|
56
|
57
|
58
|
60
|
61
|
62
|
63
|
66
|
68
|
70
|
72
|
74
|
(b) An industrial caterer had the following daily sales revenues on nine different days: Rs. 58, 42, 71, 59, 66, 49, 68, 63 and 55. Assume these revenue amounts represent a simple random sample from a normal population. Construct 99% confidence interval for mean daily sales revenue for the caterer and test the significance that average sale revenue is Rs. 60. (10)
Q. 5 (a) Define and explain the following terms: (10)
i) Test-statistic
ii) Power of test
iii) Critical values
iv) Degree of freedom
v) Level of significance
(b) A manufacturer of detergent claims that the mean weight of a particular box of detergent is 3.25 pounds. A random sample of 64 boxes revealed a sample average of 3.238 pounds with a standard deviation of 0.117 pounds. Using the 1% level of significance, is there evidence that the average weight of the boxes is different form 3.25 pounds. (10)
ASSIGNMENT No. 2
Total Marks: 100
Q. 1 (a) How will you describe the simple linear regression model. Describe the properties of least square regression line. (10)
(b) Suppose that four randomly chosen plots were treated with various levels of fertilizer resulting in the following yield of corn. (10)
Fertilizer (kg/Acre) X
|
100
|
200
|
400
|
500
|
Production (Bushels/Acre) Y
|
70
|
70
|
80
|
100
|
Fit a simple linear regression line and estimate the production when X=370 kg/acre.
Q. 2 a) Define Rank Correlation. Under what situations rank correlation is used? (05)
b) What is the relationship between regression co-efficient 
and correlation co-efficient “r”? (05)
and correlation co-efficient “r”? (05)
c) Given:
X
|
1
|
2
|
3
|
4
|
5
|
Y
|
8
|
9
|
13
|
18
|
27
|
Fit Y = a + bX by least squares method and estimate Y for X = 6. Also fit X = c + dY by least squares method. (10)
Q. 3 a) Differentiate attribute & Variable? Distinguish between A and 
, B and 
. (10)
, B and . (10)
b) 750 students appeared in an examination and 470 were successful. 465 had attended the classes and 58 of them failed. Calculate co-efficient of association between attending classes and success. (10)
Q. 4 a) Define Chi-square statistic. Also explain its importance in inferential theory. (05)
b) The following table gives the distribution of 200 school children according to physical defect 
and speech defect 
. (15)
and speech defect . (15)
Speech Defect
|
Number of Children
| ||
 |  |  | |
 |
34
|
22
|
19
|
 |
25
|
14
|
11
|
 |
21
|
18
|
26
|
Do the data suggest association, between physical defect and speech defect? Use 
as the level of significance.
as the level of significance.
Q. 5 a) What is measured by moving average? Why are 4-quarter and 12 month moving average used to develop a seasonal index? (10)
b) Fit a Quadratic parabola to the following data. (10)
Year
|
1936
|
1939
|
1942
|
1945
|
1948
|
1951
|
Price in Rs.
|
187
|
142
|
133
|
129
|
136
|
169
|
Use your result to estimate the value for year 1953.
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