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Cms 301: Advanced Business Statistics Question Paper
Cms 301: Advanced Business Statistics
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2009
1
UNIVERSITY EXAMINATIONS: 2008/2009
THIRD YEAR STAGE 1 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 301: ADVANCED BUSINESS STATISTICS (WEEKEND CLASS)
DATE: APRIL 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
(a) Identify and explain the components of a time series [8 Marks]
(b) You have the following information. Numbers of VCR sold in November were 125 but in
December were 136. Other things being equal, predict the number of VCR to be sold in
January and February respectively using a 2-month moving average approach.
[4 Marks]
(c) A random sample of 344 of nursery school pupils were asked if they can take a gift from a
stranger willingly. Eight three of the pupils returned the reply, they can. Find a 0.9 confidence
interval for the proportion of pupils who can willingly take gifts from strangers. Assume a
two-tail scenario. Interpret your result. [5 Marks]
.
(d) State and explain decision making with and without probabilities [5 Marks]
(e) On any typical school day, demand for chips in the university restaurant averages 100 plates.
This estimate may go up or down by 20 plates. If it costs KSHS 15 to prepare a plate of chips
that can be sold for 35/= per plate. Any plate of chips not sold at the end of the day, has no
value. How many plates of chips should be stocked by the university restaurant daily? (assume
2
normal distribution of plate of chips) [8 Marks]
QUESTION TWO
(a) Eight brands of rice have been ranked by groups of women in Githurai and Ruiru.
These rankings are presented below. Determine whether there is any association
between the rankings [10 Marks]
Brand A B C D E F G H
Githurai
rank
1 4 8 3 6 2 5 7
Ruiru
rank
2 6 8 1 5 4 7 3
(b) Of a random sample of 901 JKUAT graduated students, 411 were able to state their correct
degree categories (i.e. first class, upper second, lower second or pass) three years after
graduating from the university. Considering a one tail case, test at the 10% level, the null
hypothesis that at least 50% of all the graduated students are able to state their degree
categories correctly against the alternative that the population proportion is less than 50%.
Also find the p-value of this test. [10 Marks]
QUESTION THREE
Amina is a faithful reader of Friday Kenya Times newspaper. For the last 20 weeks she has been
counting the number of spelling errors in this Friday Edition. The results follow:
________________________________________________________________________
WEEK ERROS WEEK ERROS WEEK ERROS
1 12 8 21 15 7
2 19 9 14 16 18
3 8 10 7 17 12
4 11 11 13 18 13
5 15 12 19 19 13
6 17 13 11 20 20
7 11 14 10
(a) Find the sample mean number of errors for the twenty Fridays [2 Marks]
3
(b) Find the central line, lower and upper control limits for the c-chart [9 Marks]
(c) Sketch the c-chart and discuss its features [9 Marks]
QUESTION FOUR
(a) Explain Analysis of variance [3 Marks]
(b) Anakwe fitted a model on a sample of 30 families in order to explain household milk
consumption. The model had three parameters. If you are told that the total sum of squares
(SST) and regression sum of squares (SSE) were found to be SST= 162.1 and SSE = 88.2,
find the coefficient of determination, corrected coefficient of determination and coefficient of
multiple correlation [7 Marks]
(c) A soft drink company sells two kinds of drinks: regular and sugar free. A random sample
consisting of six males and six females are asked what their drink preference is. Four males
preferred the regular drink while only two females preferred the regular drink. The rest of them
preferred the sugar free drink. Is it true that females on average drink significantly more sugar
free drink than men? Test at the 5% level of significance against the two sided alternative.
[10 Marks]
QUESTION FIVE
Angelina has inherited €10,000 and must decide whether to invest it in the stock market or in a
fixed deposit investment at a rate of interest of 12% p.a. for the next year. If the stock market is
good, Angelina believes that she could get a 16% return for her money, if the market is fair she
expects a return of 10% and if the market is bad she will most likely get no return at all. The
personal analyst has estimated that the probability of a good and a fair stock market is 0.4
(a) Construct a pay off table for this problem [4 Marks]
(b) What will Angelina’s decision be if she (i) is a risk seeker (ii) a risk averter (iii) chooses
according to the expected monetary value criterion? [12 Marks]
(c) Angelina can pay her analyst for information that can help her predict the state of the stock
market accurately. What is the most that she will be willing to pay the analyst? Substantiate
your answer by showing all the workings. [4 Marks]
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