Statistics for Business Management 2 (MGSC211)
Higher Institute of Commerce and Management (HICM)
Semester: Second Semester
Level: 300
Year: 2018
I Examiner: Dr. Dobdinga C.F.
I Academic year: 2017/2018
1 Time Allowed: Three Hours
Course title: Statistics for Business Management II
Course Code: MGSC 211
Credit value: 6
INSTRUCTIONS: Answer ALL questions in the order in which they appear
Under what conditions is the central limit theorem most useful in sampling for making
statistical inferences about the population mean? (2mks)
Consider a discrete uniform population consisting of the values 1, 2, and 3. If the random variable X
represents these population values,
find how many possible samples with replacement and without replacement (link)
If the random samples of size n= 2 are drawn from this population, find out the mean and variance of the
sampling distribution.
With replacement (5mks)
Without replacement (5mks)
Question two (15 marks)
What is a Hypothesis? Explain how Hypothesis Testing is useful to management?
(2mks)
What are Type I and Type U Errors in hypothesis testing? Explain the relationship between the two types
of errors.
(3mks)
An automatic bottling machine fills oil into 2-liter (2,000 cm3) bottles. A consumer advocate wants to test
the null hypothesis that the average amount filled by the machine into a bottle is at least 2,000 cm3. A
random sample of 40 bottles coming out of the machine was selected and the exact contents of the
selected bottles are recorded. The sample mean wasl,999.6cm
3
. The population standard deviation is
known from past experience to be 1.30cm
3
.
Test the null hypothesis at an a of 5%. (5mks)
Assume that the population is normally distributed with the same standard deviation
ofl.30cm
3
. Assume that the sample size is only 20 but the sample mean is the same1,999.6cm
3
. Conduct
the test once again at an a of 5%. (4mks)
Page 1 of 2
iii) If there is a difference in the two test results, explain the reason for the difference. (1 mk)
Question three (20 marks)
THE UNIVERSITY OF BAMENDA HIGHER INSTITUTE OF
COMMERCE AND MANAGEMENT FIRST SEMESTER
EXAMINATIONS
Question one (15 marks)
a) What is a sampling distribution and what are the uses of sampling distributions? (2mks)
www.schoolfaqs.net
A child is allowed a lucky dip from each of three boxes. One box contains 10 chocolates and 15 mints,
one box contains 8 apples and 4 oranges and the third box contains 7 dinosaurs and 3 turtles. Event A, B,
C are defined as follows; A; The child gets a chocolate and a dinosaur; B: the child gets a mint or a turtle
(or both); C: the child gets an apple.
Required:
a) List the events A, B and C (10 mks)
b) Find (i) P(AAC) (ii) P(ACB) (iii) P(BDC) (iv)P(AUB) (v)P (AUC) (10 mks)
Question four (20 marks)
a) A quality control inspector collects ten manufactured items at random from a production line. The
whole production contains 10 percent of faulty items. Assume that X represents the number of faulty
items in the sample.
i) What is the expectation of the number of faulty items? (2mks)
ii) What is the variance of the number of faulty items? (2mks)
iii) What is the probability that: (i) exactly 2 items are faulty? (ii) 0 item is faulty? (iii)
More than 1 item is faulty? (6mks)
b) An employer interviews eight people for four openings in a company. Three of the eight
persons are from a minority group. If all eight are qualified, in how many ways could the employer for
the four positions if (a) the selection is random? (b) Exactly two are selected from the minority group?
(5mks)
c) In order to integrate aerobics into her exercise program, Claire can select the following
machines; treadmill, cycle and stair stepper. List all possibilities for her aerobics selection. (5mks)
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