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Introduction To Business Statistics Question Paper

Introduction To Business Statistics

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2011

INTRODUCTION TO BUSINESS STATISTICS
DATE: AUGUST 2011 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
Question One
(a) Differentiate between the following terms as applied in statistics
(i) Measures of central tendency and measures of dispersion [2 Marks]
(ii)Inferential statistics and descriptive statistics [2 Marks]
(iii) An event and an experiment [2 Marks]
(iv) Null and alternative hypothesis [2 Marks]
(v)Price index and quantity index [2 Marks]
(b) A husband and a wife appear in an interview for two vacancies in the same post. The
probability of a husband’s selection is 1/7 and that of the wife’s is 1/5.Find the probability that
(i) Both of them will be selected [2 Marks]
(ii) Only one of them will be selected [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
2
put into one bin. From the bin one item is drawn at random and it is found to be defective. Find
the probability that this item was produced on machine Y. [6 Marks]
(d) Explain five steps taken in hypothesis testing [5 Marks]
(e) The following table gives the prices and weights of different items in 2009 and 2010. Compute
the weighted cost of living index using 2009 as base period
2009 2010
Item weight Price (ksh) Price( ksh)
Bread 100 15 20
Cheese 10 100 120
Tomato sauce 1 10 20
[4 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 Marks]
(iv) Standard deviation [5 Marks]
Question Three
(a) A fruit seller found out that out of 100 oranges 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
3
(i) Draw a tree diagram to represent probability outcomes for this experiment [3 Marks]
(ii) Find the probability that all the three oranges drawn are good [2 Marks]
(iii) Find the probability that at least one of the oranges is bad [2 Marks]
(b) An ambulance service claims that it takes, on average 8.9 minutes to reach its destination in
emergency calls. To check on this claim, the agency which licenses ambulance services had them
timed on 50 minutes emergency calls, getting a mean of 9.3 minutes with a standard deviation of
1.8 minutes. At the level of significance of 0.05, does this constitute evidence that the figure
claimed is too low? [5 Marks]
(c) A financial consultant is interested in the differences in capital structure within different firm sizes
in a certain industry. The consultant surveys a group of firms with assets of different amounts and
divides the firms into three groups. Each firm is classified according to whether its total debt is
greater than stockholders’ equity or whether its total debt is less than the stockholders’ equity. The
results of the survey are shown belo
<500 500-2000 2000 Total
Debt less than equity 7 10 8 25
Debt greater than equity 10 18 17 37
Total 17 28 17 62
Do the three firm sizes have the same capital structure? Use 0.10 level of significance [8 Marks]
Question Four
(a) Differentiate between skewness and kurtosis [2 Marks]
(b) The following data shows ages of employees in an organization
Age below
(years)
20-25 25-30 30-35 35-40 40-45 45-50 50-55
Number of
employees
8 20 40 65 80 92 100
Calculate the coefficient of skewness and comment on your results [7 Marks]
(c) (i) Differentiate between Paasche’s and Laspeyre’s index numbers [3 Marks]
4
(ii) The following table shows information from the raw material purchase records of a small
factory for the year 2009 and 2010
Commodity 2009 2010
Price in $ Quantity Price in $ Quantity
A 2 8 4 6
B 5 10 6 5
C 4 14 5 10
D 2 19 2 13
Using 2009 as the base year, calculate
(i) Laspeyre’s price index [3 Marks]
(ii) Paasche’s price index [3 Marks]
(iii) Fisher’s ideal index [2 Marks]
Question Five
(a) Differentiate between correlation and regression analysis in a bi-variate data [4 Marks]
(b) The table below gives the monthly income and expenditure on food of seven households.
Income (x) 35 49 21 39 15 28 25
Food expenditure
(Y)
9 15 7 11 5 8 9
(i) 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]
(ii) Find how much a household with a monthly income of $3500 spends on food [2 Marks]
(c) In the year 2000 a firm began down sizing in order to reduce its costs. One of the results of these
cost cutting measures has been a decline in the percentage of private industry jobs that are
managerial. The following data show the percentage of females who are managers from 2000 to
2007.
Years 2000 2001 2002 2003 2004 2005 2006 2007
Percentage 5.9 5.1 4.2 6.3 6.0 7.4 5.3 6.0
5
Calculate
(i) The 2-year moving average [2 Marks]
(ii) 3-year moving average [3 Marks]

Introduction To Business Statistics Question Paper

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