MAASAI MARA UNIVERSITY
BBM 351: MANAGERIAL STATISTICS
SPECIAL / SUP EXAM
QUESTION 1 : COMPULSORY ,30 MARKS
a) Explain the characteristics of a normal distribution (5 marks)
b) Clearly, discuss three properties of a good estimator.
c) Discuss the procedure of testing the hypothesis
(6marks)
(5 marks)
d) If the mean weekly income of workers in company X follows normal probability
distribution with a mean of kshs.10, 000 and a standard deviation of kshs.1000.
i.
What is probability of selecting a worker whose income is less than
kshs.8, 000? (3 marks)
ii.
What is probability of selecting a worker whose income is between
8, 500 and 11, 500? (4 marks)
e) Intercity taxi cab co. offer services from bus station to airport. The C.E.O of the company
is considering two routes. One is through route A and the other through route B. He
wants to study the time it takes to drive to the airport using each route and then compare
the results. He collected the following sample data, which is reported in minutes in the
table below.
Route 56 67 52 45 75 54 64 60 50
A
Route 61 60 59 51 56 63 57 65 54 62
B
Using the 0.10 significance level, is there a difference in variation in the driving time for
the two routes ( 7 marks)
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QUESTION 2
a) Explain the difference between:
i. Type I and type II
(2 marks)
ii. One tailed test and two tailed test
(2 marks)
b) A tire company wishes to set a minimum mileage guarantee on its new type of tire. Tests
reveal that mean mileage is 67,900 with a standard deviation of 2,050 miles and that the
distribution of miles follows the normal probability distribution. The company wants to
set the minimum guaranteed mileage so that no more 5 per cent of the tires will be
replaced. What minimum mileage should the company announce?
(6 marks)
c) Suppose it is known that the mean annual income of workers in a certain community is
Rs.5,000 with a standard deviation of Rs.1,200. A researcher suspects the “son of soil”
workers have higher than the average income. He draws a random sample of 144 local
workers and obtains the sample mean of Rs.5,500. Can he say the local workers have
significantly higher income than the total population? (Use   0.05 ). ( 6 Marks)
d) A survey estimated that 20% of Americans aged 16 to 20 drove under the influence of
drugs and alcohol. A similar survey is planned for Kenya. They want a 95% confidence
interval to have a margin of error of 0.04. Find the necessary sample size if they expect to
find results similar to those in United States (4marks)
QUESTION 3
a) A random variable of 200 consumer accounts at a large brokerage firm is selected for the
purpose of estimating the mean number of transactions per year for each customer. The
sample mean is 12. Determine 99% confidence interval for the mean number of
transactions of all consumer accounts of the firm.
(5 marks)
b) A tire manufacturer wishes to investigate the tread life of its tires. A sample of 20 tires
driven 50,000 miles revealed a sample mean of 0.30 inch of tread remaining with a
standard deviation of 0.09 inches. Construct a 98 per cent confidence for the population
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mean. Would it be reasonable for the manufacturer to conclude that after 50,000 miles the
population mean of tread remaining is 0.34 inches?
(5 marks)
c) Two different models are available for the same machine. The production statistics
(number of units produced per hour) of these two models are given below. The data was
collected on different days.
Model A:
180,
176,
184,
181,
190,
137,
Model B:
195,
194,
190,
192,
187,
185, 187,
Will you conclude that Model A and Model B have the same productivity? ( 10 marks)
QUESTION 4
a)
Prior to an advertising campaign, 35 per cent of a sample of 400 housewives used a certain
product. After the campaign, 40 per cent of a second sample of 400 housewives used the
same product.
Required:
Did the campaign increase sales? (6 marks)
b) A manager is convinced that a new type of machine does not affect production at the
company’s major shop floor. In order to test this, 12 samples of this week’s hourly output is
taken and the average production per hour is measured as 1158 with a standard deviation of
71. The output per hour averaged 1196 before the machine was introduced.
Required:
Test the manager’s conviction (6 marks)
c) The sales Manager of a large sales force is interested in finding whether or not average
number of weekly sales contacts per sales representative
(15) has changed. The sample
information was collected and it was found that 200 sales representatives had an average of 16.5
contacts per week with a standard deviation of 3.5. At 5 per cent level of significance, what
should the sales manager conclude? (7 marks)
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QUESTION 5
a) Give some examples of the type of data that form a normal distribution.(5marks)
b) Under what conditions can the normal distribution be used as an approximation to the
binomial distribution? ( 5 marks)
c) What do confidence limits measure? ( 3 marks)
d) Because of economic conditions, a firm reports that 30 per cent of its accounts receivable
from other business firms are overdue. The firm’s policy is that if an accountant takes a
random sample of five such accounts and finds that exactly 20 per cent of the accounts
are overdue 10 per cent of the time, then a warning letter should be written to the
particular firm. Should the warning letter be written? ( 7 marks)
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