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Cms 301 Advanced Bussiness Statistics Question Paper
Cms 301 Advanced Bussiness Statistics
Course:Bachelor Of Commerce In Actuarial Science
Institution: Kca University question papers
Exam Year:2011
UNIVERSITY EXAMINATIONS: 2011/2012
YEAR 3 EXAMINATION FOR THE BACHELOR OF COMMERCE
CMS 301 ADVANCED BUSSINESS STATISTICS (SUNDAY)
DATE: APRIL 2012 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any other Two Questions
QUESTION ONE (30 Marks)
(a) Distinguish between seasonal variations and cyclical variations (4Marks)
(b) A ranch contains 1500 animals which comprise 600 dairy cattle, 450 beef cattle, 300goats and 150
sheep. Show how you would select a stratified random sample size 100 from this population in
conducting a survey. (4Marks)
(c)A manufacturer of guard uniforms wants to estimate the mean waist size for men in his city .A
sample of 2200 men yielded a mean number of 32 with a standard deviation of 10.What is the 99%
confidence interval for the population mean. (4Marks)
(d) 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. (2Marks)
(e)A car hire company manager believes that the monthly repair costs (Y) of cars are related to age (X)
of the cars. Five cars are selected randomly and from the records we obtained the following data :(x,
y)={(2,2),(3,5),(4,7),(5,10),(6,11)}.Based on our practical knowledge we hypothesize a linear
relationship between predictor X and the cost Y.
Use the sample information to estimate the unknown slope (ß) and the intercept (a) for a least squares
regression line. (7 Marks)
(f) Wafula has inherited £10,000 and must decide whether to invest in the stock market or in a fixed
deposit investment at a rate interest of 12% p.a for the next year. If the stock market is good, Papa
believes he could get a 16% return for his money, if the market is fair he expects a return of 10% and if
2
the market is bad he will most likely get no return at all. The personal analyst has estimated that the
probability of good and a fair stock market is 0.4.Construct a payoff table for this problem
(3Marks)
(g)The table below shows the number of students in each of two classes, A and B who passed and
failed an examination given to both groups.
Passed Failed
Class A 72 17
Class B 64 23
Using a 0.01 significance level test the hypothesis that there is no difference between the classes
(6 Marks)
OUESTION 2 (20Marks)
(a) Distinguish between qualitatitive and quantative techniques of forecasting (4Marks)
(b) A grocery store is open every day except Tuesdays and Sundays. The number of customers visiting
the store each day for three weeks is shown below:
Week Day Customers
1 Monday 160
Wednesday 170
Thursday 140
Friday 180
Saturday 280
2 Monday 170
Wednesday 180
Thursday 140
Friday 190
Saturday 300
3 Monday 200
Wednesday 210
Thursday 180
Friday 230
Saturday 340
3
(i)Find a five-day moving average trend (4Marks)
(ii) Using the additive model, estimate the” seasonal” factors for each of the five days
(5Marks)
(iii) Forecast the number of customers for each day of week 4. (5Marks)
(iv)Comment on the likely accuracy of your forecasts in (iii) (2Marks)
QUESTION 3 (20Marks)
(a) Define the three environments under which decisions are made. (6 Marks)
(b) A company is trying to decide whether to bid for a certain contract or not. They estimate that merely
preparing the bid will cost £10,000.If their company bid then they estimate that is there is 50%
chance that their bid will be put on the “short list”, otherwise their bid will be rejected. Once
“shortlisted” the company will have to supply further detailed information (entailing costs
estimated at £5,000).After this stage their bid will either be accepted or rejected.
The company estimates that the labour and material costs associated with the contract are
£127,000.They are considering three possible bid prices, namely £155,000,£170,000 and
£190,000.They estimate that the probability of these bids being accepted(once they have been
shortlisted) is 0.90,0.75 and 0.35 respectively.
(i) Draw a decision tree for the problem (6Marks)
(ii) What should the company do and what is the expected monetary value of your suggested
course of action? (8Marks)
QUESTION 4 (20Marks)
(a) Define any five methods of forecasting (5 Marks)
(b) (i)Define regression analysis (2 Marks)
(ii) State FOUR assumptions in regression analysis (4 Marks)
(iii)Suppose that some regression data of five elements has the following sums.
2
2
2
Sx1=153 ,Sx1=5899,Sx1y = 96387 ,Sx2 = 352 ,Sx2y= 323036,Sx = 26086,Sy=4120,Sx1x2=9697
Determine the least squares regression equation. (9 Marks)
QUESTION 5 (20Marks)
(a) Define statistical quality control and state two of its objectives. (4Marks)
4
(b)An industrial process fills containers with breakfast oats. The mean fill for the process is 510 grams
and the standard deviation of fills is 15 grams. Four containers are selected every hour and the mean
weight of the subgroup of four weights is used to monitor the process for special causes and to keep
the process in statistical quality control. Find the lower and upper control limits for the X-bar chart
(6Marks)
(c)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.
(10 Marks)
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