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Dms 201: Business Statistics I Question Paper
Dms 201: Business Statistics I
Course:Bachelor Of Commerce
Institution: University Of Nairobi question papers
Exam Year:2014
UNIVERSITY OF NAIROBI
UNIVERSITY EXAMINATIONS-2013/2014
(REGULAR/DAY/MODULE 111)
SECOND YEAR EXAMINATIONS FOR THE DEGREE OF BACHELOR OF COMMERCE
DMS 201: BUSINESS STATISTICS
DATE: JANUARY 7, 2014 TIME: 11.30A.M.- 1.30P.M.
INSTRUCTIONS
1. Answer any four questions.
2. All questions carry equal marks.
QUESTION ONE
a) Distinguish between the following:
i) Primary data and secondary data
ii) Parameter and statistics
iii) Descriptive and inferential statistics
iv) Point estimate and interval estimate
b) Mwananchi Ltd. is a diversified international company operating largely in Kenya. In 2012 they bought an art auction house. A year later they reviewed operations to see how their investment was developing. at this point they had 44 weeks of contract information and produced their first progress report and planning document. One part of this document contains the frequency distribution below:
class frequency
0-10 1
10-20 8
20-30 13
30-40 10
40-50 5
50-60 4
60-70 2
70-80 1
Required:
i) Construct a histogram and comment on the distribution
ii) Compute the mean, median and mode of the distribution
iii)Compute the variance and standard deviation of the distribution (13 marks)
QUESTION TWO
a) Briefly explain how the following are used in decision analysis:
i) Linear regression
ii) Correlation analysis
iii) Coefficient of determination (9 marks)
b) Ten experiments were done to find the effects of bonus rates paid to the sales team of a particular company. The results were as follows;
Bonus (%) 0 1 2 3 4 5 6 7 8 9
sales($000) 3 4 8 10 15 18 20 22 27 28
Required:
i) Compute the Pearson''s product moment correlation coefficient and interpret it (7 marks)
ii) Determine the regression equation that can help predict sales given bonus rate paid (6 marks)
iii)Did the estimated regression equation provide a good fit? Explain (3 marks)
QUESTION THREE
a) You are considering two azlternative investments. In both cases, you are unsure about the percentage return, but believe that your uncertainty can be represented by normal distributions with the means and standard deviations shown in the table below:
Investment Mean Standard Deviation
A 10.4 1.2
B 11.0 4.0
You want to make the investment that is more likely to produce a return of at least 10%.
Required:
Which investment should you choose? (8 marks)
b) Two machines make identical parts that are combined on a production line. The older machines makes 40% of the parts, of which 85% are of good quality; the newer machine makes 60% of the parts of which 95% are good.
Required:
i) If a part is selected at a random, what is the probability that it is faulty? (4 marks)
ii) A random check further down the production line shows an unusual fault, which suggest the particular machine that made the part needs adjusting. What is the probability that the older machine made the part? (5 marks)
c) Jane Maina knows that in the long term she has a 50% chance of making sale when calling on a customer. One morning she arranges six calls.
i) Which probability distribution best describes Jane''s situation? Explain.
ii) What is the probability that Jane will make exactly three sales?
iii) What is the probability that Jane will make fewer than two sales? (8 marks)
QUESTION FOUR
a) Explain clearly what is meant by time series. (2 marks)
b) What is the purpose of time series analysis? (2 marks)
c) Consider the following sales data (in millions of shillings) of a particular company.
QUARTER
YEAR I II III IV
1 18 28 20 30
2 36 22 20 52
3 30 25 75 30
i) Construct a graph for this data (5 marks)
ii) Would you consider using multiplicative or additive model to determine the seasonal variation? Explain. (2 marks)
iii) Find a centered four point moving average trend and place it on your graph. (4 marks)
iv) Calculate the seasonal components using the model determined in (ii) above. (4 marks)
v) Deseasonalize the sales data using the seasonal variation determined in (iv) above. And state why this is important (4 marks)
vi) Predict sales of quarters I and II of year 4. (2 marks)
QUESTION FIVE
a) Distinguish between the following:
i) Null and alternative hypotheses
ii) One tailed and two tailed tests
iii) Type I and Type II errors. (9 marks)
b) The manufacturer of steel-belted radial truck tyre claims that the mean mileage the tyre can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is 5,000 miles. A truck company bought 48 tires and found that the mean mileage for their trucks is 59,500 miles. Is the truck company''s experience different from that claimed by the manufacturer at the 0.05 significant level?
Required:
i) State the null and alternative hypothesis
ii) State the decision rule
iii) Compute the value of the test statistics
iv) What is your decision regarding Ho?
v) What is the p-value? Interpret it. (16 marks)
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