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Advanced Business Statistics Question Paper
Advanced Business Statistics
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2010
UNIVERSITY EXAMINATIONS: 2010/2011
THIRD YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 301: ADVANCED BUSINESS STATISTICS (SUNDAY)
DATE: DECEMBER 2010 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) You have the following information. Numbers of flash disks sold in November were 125 but in
December were 136.Other things being equal predict the number of flash disks to be sold in
January and February respectively using a 2 month moving average.
b) (i) List TWO major reasons for studying secular trend in time series data. (2marks)
(ii) Distinguish between seasonal variations and cyclical variations. (4marks)
c) A random sample of 344 nursery school pupils were asked if they can take a gift from a stranger
willingly. Eighty three of the pupils replied they can. Find a 0.9 confidence interval for the
proportion of pupils who can willingly take gifts from strangers. Interpret your result. (6marks)
d) (i) Explain two types of errors in hypothesis testing. (3marks)
(ii)During a statistics class, a student developed the following hypothesis statements for a research
on the 330ml Noxida soft drink.
H0:µ=330 ml
H1:µ?330 ml
The following information was obtained from a sample of 11 bottles.
324 330 328 331 333 325 330 312 329 322 332
Using a significance level of 0.05, determine whether the null hypothesis should be rejected.
(5marks)
e) (i) Explain THREE decision making environments. (6marks)
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(ii) Wote credit bank Ltd. Has been approached by a customer for a loan of sh.10,000 for a year.
The bank currently charges interest at 16% PER annum. f loan is not granted then the sh, 10,000 can be
invested in the money market paying interest at the rate of 8% per annum.From past records it is
estimated that 5% of customers default on loan paymenti.e no interest or capital is paid .
Draw a decision tree for this problem and advice the bank accordingly on whether they should
grant the loan. (5marks)
f) Define the term ‘acceptance sampling as used in quality control.
(2marks)
QUESTION TWO
a) Differentiate between inspection and semi-average method of projecting the trends in time series
analysis. (4marks)
b) Explain the meaning of the term ‘forecasting’ (2marks)
c) Distinguish between quantitative and qualitative techniques of forecasting (4marks)
d) The sales of a Pentium II computer for a certain firm over the last 13 months are shown in table II.
Table II
Month 1 2 3 4 5 6 7 8 9 10 11 12 13
Sales
(units)
450 440 460 410 380 400 370 360 410 450 470 490 460
(i) Using a three months period, calculate the sales forecasts for the 4th month and above using the
moving averages. (4 marks)
(ii) Using the forecasts produced for the 7th to the 13th month; calculate the mean squared error for the
forecast errors. (6 marks)
QUESTION THREE
a) Write short notes on the following
i. Population in statistics
ii. Random sample
iii. Critical region
iv. Confidence interval (8 marks)
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b) The height of students in a certain BCOM class is nod with mean µ and standard deviation d .A
random sample of 100 students was taken and the 90% confidence interval for µ was found to be
between 175cm and 180cm.
Estimate the :-
(i) value of the sample mean
(ii) value of d
(iii) 95% confidence interval for µ (12marks)
QUESTION FOUR
a) (i) Define statistical quality control and state two of its objectives.
(ii) Distinguish between chance causes of variation and assignable causes of variation. (8marks)
b) Ten samples of five pieces were taken at regular intervals from a process
Sample
Number
1 2 3 4 5 Sample
Mean(X)
Range
(R)
1 7.47 7.48 7.47 7.49 7.48 7.478 0.02
2 7.48 7.49 7.50 7.48 7.49 7.488 0.02
3 7.49 7.48 7.50 7.48 7.49 7.498 0.02
4 7.49 7.49 7.50 7.50 7.51 7.498 0.02
5 7.49 7.49 7.51 7.49 7.51 7.498 0.02
6 7.49 7.50 7.51 7.49 7.50 7.498 0.02
7 7.50 7.50 7.51 7.51 7.50 7.504 0.01
8 7.51 7.50 7.50 7.50 7.52 7.506 0.02
9 7.51 7.51 7.52 7.51 7.51 7.512 0.01
10 7.51 7.51 7.52 7.53 7.51 7.518 0.02
Calculate
(i)The control limits for X and R (A 2 = 0.5768,D 4 =2.115,D 3 =0)
(ii) Represent X and R on a chart
(iii) Comment on the state of the process. (12 marks)
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QUESTION FIVE
a) A tax consultant hypothesize that the income tax evasion depended on;
i. The true income ( 1 x )
ii. The marginal tax rate ( 2 x )
iii. The penalty of tax ( 3 x )
iv. The probability of detection ( 4 x )
He performed a multiple linear regression and got the following result
Variables Coefficient
estimates
Standard error
Constant -52.59 7.6774
1 x 33.44 2.3937
2 x 0.93 0.1465
3 x -0.20 0.0683
4 x -1.48 0.3795
b) Write down the model for the above output. (2marks)
c) Calculate the t-ratio and the 95% confidence interval for each regression coefficient. (10marks)
d) State whether 1, x 2 x , 3 x and 4 x are statistically significant in explaining the variation of the response
variable Y. (8marks)
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