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Econ 234: Economics Statistics Ii Question Paper
Econ 234: Economics Statistics Ii
Course:Bachelor Of Science In Economics And Statistics
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
SECOND YEAR EXAMINATION FOR THE AWARD OF
DEGREE IN BACHELOR OF SCIENCE ECONOMICS AND STATISTICS & BACHELOR OF ECONOMICS AND MATHEMATICS
ECON 234: ECONOMICS STATISTICS II
STREAMS: ECON & STAT, ECON&MATHS, ECON&SOCIO, AGRIC ECON Y2S2 TIME: 2 HOURS
DAY/DATE: MONDAY 12/8/2013 11.30 AM- 1.30 PM
INSTRUCTIONS:
Answer Question ONE and any other TWO
Do not write on the Question Paper.
Question 1 (30 marks)
(a) Distinguish purposive sampling and systematic sampling [4 Marks]
(b) Differentiate the following terms using relevant examples.
(i) Sampling distribution of x ¯ and sampling distribution of p ^. [4 Marks]
(ii) Probability distribution of discrete random variable and probability density function of a continuous random variable. [4 Marks]
(c) The random variable X has a p.d.f
F(x) = k(4-x) 1=X=3
0 otherwise
(i) Find the value of K [2 Marks]
(ii) Find p(1.2=x=2.4) [2 Marks]
(d) The mean lifetime of a sample of 100 light tubes produced by a company is found to be 1580 hours with standard deviation of 90 hours. Test the hypothesis that the mean lifetime of the tubes produced by the company is 1600 hours. [5 Marks]
(e) Assume that on an average one telephone line out of fifteen is busy. What is the probability that six selected telephone lines are called?
(i) More than three will be busy [2 Marks]
(ii) At most two will be busy [2 Marks]
(f) The human resource department of a company has records which show the following analysis of its 200 engineers.
Age Bachelors degree only Masters degree
Under 30 90 10
30 – 40 20 30
Over 40 40 10
If an engineer is picked at random, find the probability that
(i) He is under 40 and has a bachelor’s degree only. [2 Marks]
(ii) Has a masters degree given he is over 40 years [1 Mark]
(iii) Check if age 30 to 40 and master’s degree are independent events [2 Marks]
Question 2 (20 Marks)
(a) A sample of employees of Makali Industries were surveyed regarding the acceptance of a new pension plan the results are shown below
Opinion regarding new pension plan
Age Superior Very good Good Fair Unsatisfactory
20 up to 30 19 27 25 52 8
30 up to 40 10 17 15 29 27
40 up to 50 51 40 31 21 41
50 and over 142 81 16 9 8
Is there a relationship between age and an employee’s opinion of the new plan? Test at 1% significance level (follow the hypothesis testing procedure) [14 Marks]
(b) A company that manufactures exercising machines wanted to know the percentage of large companies that provide health club facilities. A sample of 180 such companies showed that 96 of them provide health club facilities. Construct a 98% confidence interval for the percentage of such companies that provide health club facilities.[6 Marks]
Question 3 (20 Marks)
(a) The average trade in value of a particular make of used car depreciates with time according to the following table which the values of X may be assumed to be exact.
Age x 2.0 2.5 3.0 3.5 4.5 5.0 6.0 7.0
Value (sh 000) y
610 555 509 465 389 351 310 250
(i) Find the regression line y ^=a+bx
(ii) Interpret the values of b_0 and b_1
(iii) Calculate the Karl Pearson’s product moment correlation coefficient. Comment on the value. [12 Marks]
(b) A sociologist claims that the mean age at which all children start walking is 12.5 months. Pinny a research student took a sample of 20 children to test this claim. He found that the mean age at which these children started walking was 12 a months with a standard deviation of 0.4 months. Using 1% significance level can you conclude that the mean age at which al children started walking is greater than 12.5 months? [8Marks]
Question Four (20 Marks)
(a) A random sample is selected from each of three makes of ropes and their breaking strength are measured with the following results.
I II III
70 100 60
72 110 65
75 108 57
80 112 84
83 113 87
120 73
107
Test at 5% significance level whether the breaking strength of the ropes differ significantly. [12 Marks]
(b) The following table gives the number of days in a 50 – day period during which automobile accidents occurred in a city. Fit Poisson distribution to the data.
[8 Marks]
No of accidents 0 1 2 3 4
No of days 21 18 7 3 1
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