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Introduction To Business Statistics Question Paper

Introduction To Business Statistics

Course:Bachelor Of Commerce

Institution: Kca University question papers

Exam Year:2011

UNIVERSITY EXAMINATIONS: 2010/2011
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 105INTRODUCTION TO BUSINESS STATISTICS
DATE: DECEMBER2011 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any Other Two Questions
Question One
(a) Explain the difference between the following terms
(i) An event and an experiment [2 Marks]
(ii) Observed and the Expected frequencies for a goodness of fit [2 Marks]
(iii) Type I and type II errors [2 Marks]
(b) X and Y are two events such that P(X/Y) =0.4, P(Y) =0.25 and P(X) =0.2
Find;
(i) P(X nY) [3 Marks]
(ii) P(X ?Y) [3 Marks]
(c) An item is manufactured by three machines X, Y and Z. all the machines have equal
capacity and are operated at the same rate. It is known that the percentage of defective
items produced by X, Y and Z. are 2, 7 and 12 percent respectively. All the items produced
by X, Y and Z. are put into one bin. From the bin one item is drawn at random and it is
2
found to be defective. Find the probability that this item was produced on machine Y.
[6 Marks]
(d) The owner of a small shop selling food items collected the following information regarding
the price and quantity sold for particular items
1999 2000
Commodity Price Quantity Price Quantity
A 2 8 4 6
B 5 10 6 5
C 4 14 5 10
D 2 19 2 13
Calculate Laspeyre index and Paasche index [6 Marks]
(e) A fruit seller found out that out of 100 apples in a box, 10 were bad and could not be
sold.3 fruits are drawn at random by a customer, one at a time, replacing the
previous one each time
(i) Draw a tree diagram to represent probability outcomes of this experiment
[2 Marks]
(ii) Find the probability that all the three apples drawn are good [2 Marks]
(iii) Find the probability that at least one of the apples is bad [2 Marks]
Question Two
The following data represents the weekly wages in hundred Kenya shillings of employees of ABC company:
30, 42, 30, 54, 40, 48, 15, 17, 51, 42, 25, 42,
31, 27, 25, 36, 29, 27, 38, 31, 43, 32, 36, 40,
36, 22, 30, 31, 19, 48, 16, 42, 32, 21, 22, 46,
33, 41, 21. 22
Construct a frequency distribution with 8 equal classes [4Marks]
Hence determine the
(i) Mean [3 Marks]
(ii) Mode [4 Marks]
(iii) Median [4 Mark]
(iv) Standard deviation [5 Marks]
Question Three
(a) A manufacturer makes writing pens. The manufacturer employs an inspector to check the
quality of his product. The inspector tested a random sample of the pens from a large batch
and calculated the probability of any pen being defective as 0.025. Ms Nyangi buys two
pens made by the manufacture. Calculate
(i) The probability that both pens are defective [3 Marks]
(ii) The probability that exactly one of the pens is defective [4 Marks]
(b) Suppose 80 per cent of the material received from a vendor is of exceptional quality, while only 50 per cent of the material received from vendor B is of exceptional quality. However,the manufacturing capacity of vendor A is limited and for this reason only 40 per cent ofthe material purchased comes from vendor A. The other 60 per cent comes from vendor B.
An incoming shipment of material is inspected and it is found to be of exceptional quality.
What is the probability that it came from vendor A. [6 Marks]
(c) Explain any TWO limitations of time series analysis [4 Marks]
(d) Briefly explain two application areas of time series in business [3 Marks]
Question Four
(a) Differentiate between Null hypothesis and alternative hypothesis [2 Marks]
(b) A battery manufacturing company claims that its top of the line Batteries are good, on
average for at least 65 months. A consumer protection agency tested 15 such batteries to be
63 months with a standard deviation of 2 months. At 5% level of significance can we
conclude that the claim of the company is true? [7 Marks]
(c) The table below gives the monthly income and expenditure on food of seven households.
4
Income (x) 35 49 21 39 15 28 25
Food expenditure
(y)
9 15 7 11 5 8 9
Find the least square regression line for the data on incomes and food expenditures. Take
income as independent variable and food expenditure as a dependent variable. [9 Marks]
(i) Find how much a household with a monthly income of $3500 spends on food [2 Marks]
Question Five
(a) Explain FIVE steps involved in testing a hypothesis [5 Marks]
(b) A manufacturing company believes that the batteries for laptop computers produced by
process A on average last longer than batteries for laptop computers produced by process
B. To test this belief, random samples of laptop computer batteries produced by the two
processes were tested and yielded the results below
Process Sample size Average lifetime (in
minutes of usage)
Standard
Deviation in Km
A 64 106 12
B 64 100 10
Determine whether there is evidence at 5% level of significance that the firm is correct in its belief.
[6 Marks]
(c) Two investigators have studied the income of a group of persons by the method of
sampling. The following table gives their findings
Investigator Poor Middle
Class
Well-to-do Total
A 160 30 10 200
B 140 120 40 300
Total 300 150 50 500
Using the Chi-squared test, show that the sampling technique of at least one of the investigators is a suspect. [9 Marks]

Introduction To Business Statistics Question Paper

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