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Hbc 2121: Introduction Business Statistics Question Paper
Hbc 2121: Introduction Business Statistics
Course:Bachelor Of Commerce
Institution: Dedan Kimathi University Of Technology question papers
Exam Year:2013
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DEDAN KIMATHI UNIVERSITY OF TECHNOLOGY
UNIVERSITY EXAMINATION 2012/2013
FIRST YEAR SPECIAL/SUPPLEMENTARY EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE/BACHELOR BUSINESS ADMINISTRATION
HBC 2121: INTRODUCTION BUSINESS STATISTICS
DATE: 9TH JULY 2013 TIME: 2.00PM – 4.00PM
INSTRUCTIONS: Answer question ONE (COMPULSORY) and any other TWO
Question One(30 Marks)
a. Define the following terms as used in business statistics.
i. Skewness and Kurtosis. (2 marks)
ii. Discrete and continuous variable. (2 marks)
b. Discuss the components of a time series. (4 marks)
c. A work-standards expert observes the amount of time required to prepare a sample of 10 business letters in an office, with the following results listed in ascending order to the nearest minute: 5, 5, 5, 7, 9, 14, 15,15, 16, 18. Determine the;
i. Mean, (2 marks)
ii. Median, and (2 marks)
iii. Mode for this group of values. (1 mark)
d. The table below identifies the probability that a computer network will be inoperative the indicated number of periods per week during the initial installation phase for the network.
Number of periods (X)
4
5
6
7
8
9
Probability [P(X)]
0.01
0.08
0.29
0.42
0.14
0.06
Calculate;
i. the expected number of times per week that the network is inoperative and (2 marks)
ii. the standard deviation for this variable. (2 marks)
e. Out of 12accounts held in a file, four contain a procedural error in posting account balances.
i. If an auditor samples one account randomly, what is the probability that it will contain the error? (3 marks)
ii. If an auditor samples two accounts randomly, what is the probability that at least one will contain the error? (5 marks)
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iii. If an auditor samples three accounts randomly, what is the probability that at least
one will contain the error? (5 marks)
Question Two (20 Marks)
a. The breaking strengths of cables produced by a manufacturer have a mean of 1800 pounds
(lb) and a standard deviation of 100 lb. By a new technique in the manufacturing process, it
is claimed that the breaking strength can be increased. To test this claim, a sample of 50
cables is tested and it is found that the mean breaking strength is 18501b. Can we support
the claim at the 0.01 significance level? (6 marks)
b. Suppose that a stock analyst derives the following probability distribution for the earnings
per share (EPS) of a firm.
EPS($) P(x) EPS($) P(x)
1.50 0.05 2.25 0.15
1.75 0.30 2.50 0.10
2.00 0.35 2.75 0.05
Calculate the;
i. Expected value for earnings per share. (4 marks)
ii. Standard deviation for earnings per share (6 marks)
c. Explain any four Non-parametric tests. (4 marks)
Question Three (20 Marks)
a. Distinguish between Type I and Type II error. (2 marks)
b. Explain the methods of random sampling. (6 marks)
c. An economist is studying the job market in Nyeri area neighborhoods. Let x represent the
total number of jobs in a given neighborhood and let y represent the number of entry level
jobs inthe same neighborhood. A sample of six Nyeri neighborhoods gave the following
information (units in 100s of jobs).
x 16 33 50 28 50 25
y 2 3 6 5 9 3
i. Draw a scatter diagram representing the data. (4 marks)
ii. Find the equation of the least squares line y ? a ? bx . (6 marks)
iii. For a neighborhood with x = 40 jobs, how many are predicted to be entry level jobs?
(2 marks)
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Question Four (20 Marks)
a. A sample of 20 production workers in a company earned the following net pay amounts after all deductions for a given week, rounded to the nearest dollar and arranged in ascending order: $290, 340, 280, 240, 240, 255, 240, 240, 240, 255, 265, 265, 280, 240, 240, 300, 305, 325, 330,and 240. Calculate the;
i. Mean wage, (2 marks)
ii. Median wage, and (2 marks)
iii. mode. (1 mark)
b. The table below shows the values of household spending (in billions of dollars) during a 5-year period.
Year
1999
2000
2001
2002
2003
Household spending
686.9
697.2
723.7
716.6
734.5
Calculate the index numbers when 2000 is taken as the base year and give a brief interpretation. (5 marks)
c. In Nyeri County, 51% of the adults are males. One adult is randomly selected for a survey involving credit card usage.
i. Find the prior probability that the selected person is a male. (1 mark)
ii. It is later learned that the selected survey subject was smoking a cigar. Also, 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars (based on data from the Substance Abuse and Mental Health Services Administration). Use this additional information to find the probability that the selected subject is a male. (5 marks)
d. Distinguish between Value index and Paasche price index. (4 marks)
Question Five(20 Marks)
a. Discuss the methods used in estimation of trend. (6 marks)
b. Of 300 business students, 100 are currently enrolled in accounting and 80 are currently enrolled in business statistics. These enrollment figures include 30 students who are in fact enrolled in both courses. What is the probability that a randomly chosen student will be enrolled in either accounting (A) orbusiness statistics (B)? (4 marks)
c. A well-designed and safe workplace can contribute greatly to increased productivity. It is especially important that workers not be asked to perform tasks, such aslifting, that exceed their capabilities. The accompanying data on maximum weight of lift (MAWL, in kg) for a frequency of four lifts/min was reported in the article “The Effects of Speed, Frequency, and Load on Measured Hand Forces for a Floor-to-Knuckle Lifting Task” (Ergonomics, 1992: 833–843); subjects were randomly selected from the population of healthy males age 18–30. Assuming that MAWL is normally distributed, does the following data suggest that the population mean MAWL exceeds 25?
25.8
36.6
26.3
21.8
27.2
Test the hypothesis test using a significance level of 0.05. (10 marks)
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