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Bcom 373: Business Statistics Ii Question Paper
Bcom 373: Business Statistics Ii
Course:Bachelor Of Commerce
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
THIRD YEAR EXAMINATION FOR THE AWARD OF
DEGREE OF BACHELOR OF COMMERCE
BCOM 373: BUSINESS STATISTICS II
STREAMS: BCOM Y3S2 TIME: 2 HOURS
DAY/DATE: MONDAY 12/8/2013 8.30 AM – 10.30 AM
INSTRUCTIONS:
Attempt question ONE and any other TWO
Do not write on the Question Paper
QUESTION 1 (30 Marks)
(a) Explain, giving relevant examples the difference between stratified and convenient sampling methods. [4 Marks]
(b) The distribution of marks for 180 students in statistics exams showed normal distribution, with mean marks of 52 and standard deviation of 5. Calculate the number of students who scored
(i) Between 48 marks and 62 marks [2 Marks]
(ii) More than 55 marks [2 Marks]
(iii) The number of students who failed in this examination if the pass mark was 40 marks. [2 Marks]
(c) A manager in charge of research and development department of beauty Products Company seeks your input about three ways; he can use statistics in this field to benefit the company. Discuss.
[3 Marks]
(d) A study was conducted among 200 children who suffered a certain skin disease. The table below showed the results.
Parent status
Child status Both parents One parent No parent
Male 7 81 12
Female 20 65 15
Find the probability that a child picked at random
(i) Had one parent [1 Mark]
(ii) Had both parents given she is a female [2 Marks]
(iii) Had no parent and is a male [1 Mark]
(iv) Prove if the events the parent and male are statistically independent. [2 Marks]
(e) Differentiate the terms
(i) Sampling distribution and probability distributions
(ii) The significance level of a test and power of a test. [4 Marks]
(f) The following nine items are ages of worker in a finance department,
45, 47, 50, 52, 48, 47,49,53,50 obtain the 95% confidence limits for the population mean.
[7 Marks]
QUESTION 2 (20 Marks)
(a) In a study of market penetration, the marketing division of a company selected random samples of 200, 150, and 300 consumers from three cities and obtained the data in the table below. Do the data indicate that the extent of market penetration in the three cities is independent of the consumers knowledge of the product? [15 Marks]
Never heard of product Group heard but did not buy Bout it at least once Total
City
1 36 55 109
2 45 56 49
3 54 78 168
(b) Explain the concept of “auto correlation” and its use for time series analysis. Give an example of a single variable with two different time lags. [5 Marks]
QUESTION 3 (20 Marks)
The following data represent the number of units of production per day turned out by five different workers using four different types of machines
Machine type
Workers A B C D
1 44 36 48 38
2 48 40 56 44
3 37 38 40 36
4 45 34 45 32
5 40 44 50 40
At 5% level of significance test whether
(a) The mean productivity is the same for the four different machine types
(b) The five workers differ in respect to mean productivity. [20 Marks]
QUESTION 4 (20 Marks)
(a) Given the following data,
(i) Develop the estimating equation best describing these data
(ii) If an employee scored 83 on the aptitude test and had a prior experience of 7 years, what performance evaluation would be expected?
Employee A B C D E F
Performance evaluation(X1) 28 33 21 40 38 46
Aptitude Test Score (X2) 74 87 69 69 81 97
Prior Experience (X3) 5 11 4 9 7 10
[10 marks]
(b) An experimenter want to determine which of the 4 safty design would provide the best protection in case of accident of lead on collision at speed of 100km/h simulated accident are performed and the following data was collected. Each observation is composite index of passenger injuries.
Design Observation Total
1 37 42 45 49 50 45 268
2 49 38 40 39 50 51 257
3 33 34 46 38 47 36 228
4 41 48 40 42 38 41 250
1003
Test at ? = 5% H_o: T_1=T_2=T_3=T_4
H_1:T_i?T_j for i?J [10 Marks]
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