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Bmgt 220: Business Statistics Ii Y2s2 Question Paper
Bmgt 220: Business Statistics Ii Y2s2
Course:Bachelor Of Commerce
Institution: Kabarak University question papers
Exam Year:2010
INSTRUCTIONS
Answer question ONE and any other TWO questions
QUESTION ONE
(a) Explain the following distributions and explain when each is applied
i.) t-distribution (5mks)
ii.) Chi-square distribution (5mks)
(b) Explain what you understand by the following concepts
i.) Random Variable (2mks)
ii.) Expected value (2mks)
iii.) Hypothesis (2mks)
iv.) Significance level (2mks)
v.) Confidence level (2mks)
vi.) Random error (2mks)
vii.) Systematic error (2mks)
(c) Ndegwa, a salesman in industrial chemicals, had sales of Ksh20, 000. The industrial
chemical department had mean sales of Ksh12, 000 and a standard deviation of
Ksh4,000. On the other hand, Kamau, a sales person in office supplies department
had sales of Ksh10, 000. The office supplies department had mean sales of Ksh4, 000
and a standard deviation of Ksh2, 000. Compare their performance (4mks)
(d) In a given business venture, a person is able to make a gain of Ksh.3000 with a
probability of 0.65 or take a loss of Ksh.1000. What is the person’s expected value if
he/she gets involved in the venture? (2mks)
QUESTION TWO
(a) (i) Distinguish between Permutation and Combination indicating two areas where
each is applied in real life (5mks)
(ii) A consumer is requested to rank in order of preference the taste of seven
brands. If she is indifferent among these brands, what is the probability that an
individual who is truly indifferent will select a specific ordering for first three
brands? (3mks)
(iii) Given letters ABC, show in how many ways these letters can be permutated
and demonstrate using a tree diagram (2mks)
(b) Suppose Kabarak has bought 4000 bulbs. The lifetime of the bulbs has historically
been realized to be normally distributed with mean of 8000 hours and a standard
deviation of 1500 hours. How many bulbs are expected to fail in the first 6000 hours
(6mks)
(c) A man wishes to insure his ksh3,000,000 worth house against fire. The yearly
premium which he must pay to insure the house is ksh2000. If the probability that fire
will destroy his house is 1/5,000, can this be termed a fair insurance contract? (4mks)
QUESTION THREE
(a) An advertising company estimates, historically, its monthly sales to have averaged
Ksh. 36 million per depot with a standard deviation of Ksh. 10 million. As a
result of a sharp rise in competition from similar firms, a random sample of 36
depots was taken this year and gives mean sales of Ksh. 32 million. Test if the
reduction in the company sales is significant? (6mks)
(b) (i) What are the desirable properties of confidence intervals? (3mks)
(ii) A random sample of 16 observations from a normal population with standard
deviation of 6 had a mean of 25. Find a 99 percent confidence interval for the
population mean (4mks)
(c) A pharmaceutical company supposes that 40 percent of the population prefers its
medicine than any other medicine. A random sample of 400 people showed that 45
percent prefer the company’s medicine. Test whether the company’s market share has
significant grown at 1% level (7mks) Page 4 of 5
QUESTION FOUR
(a) (i) What is correlation? (2mks)
(ii) Suppose five students have the following grades in two courses:
Statistics Theory
85 93
60 80
73 65
40 50
90 75
Calculate and interpret the rank correlation coefficient (6mks)
(b) Mall supermarket CEO intends to establish if there are any significant differences
between regions in terms of the degree of acceptance of a new product. Using a
sample and the questionnaire technique, his statistician obtained the following data:
Region
Degree of acceptance East West
Poor 21 36
Moderate 83 56
Strong 24 17
i.) Determine the expected frequencies (3mks)
ii.) Calculate the Chi-Square statistic (4mks)
iii.) Test the null hypothesis that the degree of acceptance does not differ from
region to region at 5 percent significance level and give the conclusion of the
findings? (4mks)
(c) Why do we find it necessary to incorporate the error term in a statistical model (1mk)
Page 5 of 5
QUESTION FIVE
(a) (i) What is regression? (2mks)
(ii) Given the following data on quantity–price relationship:
Quantity Price
69 9
76 12
52 6
56 10
57 9
77 10
58 7
55 8
67 12
53 6
72 11
64 8
i.) Estimate the regression function (6mks)
ii.) Is it a demand or supply function? Explain (2mks)
iii.) Explain what the function means (2mks)
iv.) Is the function consistent with theory? (2mks)
v.) Calculate the average price elasticity for the relationship and comment (3mks)
(b) Write short notes on Binomial distribution (3mks)
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