ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Statistics)
WARNING
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 ASSIGNMENT(S) BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.
Assignment Submission Schedule
6 Credit Hours Due Date 3 Credit Hours Due Date
Assignment 1 14-07-2023
Assignment 1 09-08-2023
Assignment 2 09-08-2023
Assignment 3 04-09-2023
Assignment 2 29-09-2023
Assignment 4 29-09-2023
Note: Tutorial Schedule and Rehnama-e-Tulba are available on AIOU website i.e. aiou.edu.pk
Course: Business Statistics (1430) Semester: Spring, 2023
Level: BA/B.Com/BBA
1
Total Marks: 100 Pass Marks (BA/B. Com): 40
Pass Marks (BBA): 50
ASSIGNMENT No. 1
(Units 1–4)
Q. 1 (a) Differentiate between populations and samples, and describe some advantages
of samples over populations. (10)
(b) Why a frequency distribution is constructed? Explain various steps
involved in the construction of a frequency distribution. (10)
Q. 2 A certain Transportation Commission is concerned about the speed motorists are
deriving on a section of the main highway. Here are the speeds of 45 motorists:
15 32 45 46 42 39 68 47 18 31 48 49
56 52 39 48 69 61 44 42 38 52 55 58
62 58 48 56 58 48 47 52 37 64 29 55
38 29 62 49 69 18 61 55
Use these data to construct relative frequency distributions using 5 equal intervals
and II equal intervals. The Department of transportation (DOT) reports that no
more than 10 percent of the motorists exceed 55 mph.
(a) Do the motorists follow the DOT's report about driving pattern? Which
distribution did you use to answer this part? (10)
(b) The DOT has determined that the safest speed for this highway is more than
36 but less than 59 mph. What percent of the motorists drive within this
range? Which distribution did you use to answer this part?
(10)
Q. 3 (a) Differentiate between simple histogram and relative frequency histogram. (10)
(b) Here is a frequency distribution of length of phone calls made by 175
people during a Labor Day weekend. Construct histogram and
frequency polygon for these data. (10)
Length in
1–7 8–14 15–21 22–28 29–35 39–42 43–49 50–56
Minutes
Frequency 45 32 34 22 16 12 9 5
Q. 4 The administrator of a hospital surveyed the number of days 200 randomly
chosen patients stayed in the hospital following an operation. The data are.
Hospital stay in Days 1–3 4–6 7–9 10–12 13–15 16–18 19–21 22–24
Frequency 18 90 44 21 9 9 4 5
(a) Calculate mean, standard deviation and coefficient of variation. (10)
(b) According to Chebyshev's theorem, how many stays should be between 0
and 17 days? How many are actually in that interval? (05)
2
(c) Because the distribution is roughly bell-shaped, how many stays can we
expect between 0 and 17 days? (05)
Q. 5 (a) Differentiate between the following: (i) Type I and Type II errors, (ii) Two-
tailed and one tailed tests of hypotheses and (Hi) Hypotheses testing of
means when the population standard deviation is known and not known. (10)
(b) For a sample of 60 women taken from population of over 5000 enrolled in a
weight-reducing program, 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)
Total Marks: 100 Pass Marks (BA/B. Com): 40
Pass Marks (BBA): 50
ASSIGNMENT No. 2
(Units 5–7)
Q. 1 (a) How we chose a significance level in hypotheses testing? Explain the
concept of prob value, also called p-value, in this regard. (10)
(b) Two research laboratories have independently produced drugs that provide relief
to arthritis sufferers. The first drug was tested on a group of 90 arthritis sufferers
and produced an average of 8.5 hours of relief, and a sample standard deviation
of 1.8 hours. The second drug was tested on 80 arthritis sufferers, producing an
average of 7.9 hours of relief, and a sample standard deviation of 2.1 hours. At
the 0.05 level of significance, does the second drug produce a significantly
shorter period of relief? (10)
Q. 2 (a) Differentiate between regression and correlation analyses. (10)
(b) A Health Club has been advertising a rigorous program for body
conditioning. The club claims that after one month in the program, the
average participant should be able to do 8 more push-ups in 2 minutes than he
or she could do at the start. Does the random sample of 10 program
participants given below support the clubs claim? Use 0.025 level of
significance (10)
Participant 1 2 3 4 5 6 7 8 9 10
Before 38 11 34 25 17 38 12 27 32 29
After 45 24 41 39 30 44 30 39 40 41
Q. 3 In finance, it is of interest to look at the relationship between Y, a stock's
average return and X, the overall market return. The slop coefficient computed
by linear regression is called the stock's beta by investment analysis. A beta
greater than I indicates that the stock is relatively sensitive to changes in the
market; a beta less than I indicates that the stock is relatively insensitive to
changes in the market. For the following data:
Y (%) 10 12 8 15 9 11 8 10 13 11
X (%) 11 15 3 18 10 12 6 7 18 13
3
(a) Compute the beta and test to see whether it is significantly less than I at the
0.05 level of significance. (05)
(b) Test whether the correlation coefficient for this data is significantly different
from zero at 0.01 level of significance. (15)
Q. 4 (a) Define an index number and explain its various types. (10)
(b) The Bookster Publishing Company began its business of publishing college
text books in 1993. It is interesting in determining how its sales have
changed to its first year. A summary of the company's records shows how
many new books it published in each year in the following areas: (10)
1993 1994 1995
Biology 48 53 50
Mathematics 32 37 35
History 19 IS 22
English 16 20 21
Sociology 24 18 26
Physics 10 26 32
Chemistry 27 26 30
Philosophy 11 8 15
Use 1993 as the base year, calculate the unweighted aggregates quantity index
for 1994 and 1995. Interpret the results for the publishing company.
Q. 5 InfoTech has researched the unit price and total value of memory chips imported
into the United States in 1994 and 1996 as the following:
Product Price (1994) Price (1996) Total Dollar Value (000) 1994
1-megabyte chips $ 42 $65 957
4-megabyte chips $ 180 $ 247 487
16-megabyte chips $ 447 $612 349
(a) Calculate the unweighted average of relatives price index for 1996 using
1994 as the base period. (10)
(b) Calculate weighted average of relatives price index number for 1996 using
the dollar value for each product in 1994 as appropriate set of weights and
1994 as base year. (10)
