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Aec 303 : Statistics For Economists Ii Question Paper
Aec 303 : Statistics For Economists Ii
Course:Bachelor Of Commerce
Institution: Kenyatta University question papers
Exam Year:2009
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KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2008/2009
SECOND SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
AEC 303 : STATISTICS FOR ECONOMISTS II
DATE: TUESDAY 15TH SEPTEMBER 2009 TIME: 8.00 A.M. – 10.00 A.M.
INSTRUCTIONS:
Answer Question ONE and any other TWO Questions.
Question One (Compulsory)
a) Differentiate the following terms. (8 marks)
i) Estimators Vs. Estimates
ii) Parameter Vs. Statistic
iii) t-distribution Vs. standard normal distribution
iv) Correlation coefficient Vs. Coefficient of determination
b) For a random sample of 100 workers in a plant employing 1200, 70 prefer providing
for their own retirement benefits over belonging to a company-sponsored plan. Find
the 95% confidence interval for the proportion of all the workers in the plant who
prefer their own retirement plans. (5 marks)
c) Simple observations over the last 80 hours have shown that 800 customers enter a
certain bank. What is the probability that 5 customers will arrive in the bank during
the next one hour? (3 marks)
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d) Gatheris medical students’ records the number of heart attacks suffered by males
and females of various age groups in a city as follows:
_____________________________________________
Age Group Male Female Total
_____________________________________________
<30 10 10 20
30 – 60 50 30 80
>60 30 20 50
_____________________________________________
Using the above information, test whether the age and sex are independent in the
occurrence of heart attacks at 1% level of significance. (5 marks)
e) The government antipollution spokesman asserts that more than 80% of the plants in
the region meet the antipollution standards. An antipollution advocate does not
believe the government claim. She takes a random sample of published data on
pollution emission for 64 plants in the area and finds that 56 plants meet the pollution
standards.
i) Do the sample data support the government claim at 5% level of
significance? Interpret your answer. (6 marks)
ii) Would the conclusion change if the sample had been 124, but with the
sample proportion of the firms meeting the pollution standards the same as
before? (3 marks)
Question Two
a) i) What is normal distribution. (2 marks)
ii) State four characteristics of a normal distribution. (4 marks)
iii) Under what conditions can we Not Use the normal distribution but we can
use the t-distribution to find confidence intervals for the unknown population
mean? (3 marks)
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b) A company sells identical tooth paste in three different wrappings at the same
price. The sales for five months are given in the table below. Show whether
the consumer perceives the tooth paste in the three different wrappings as
different. (11 marks)
___________________________________________________
Wrapping I Wrapping II Wrapping III
____________________________________________________
87 78 90
83 81 91
79 79 84
81 82 82
80 80 88
____________________________________________________
Question Three
a) What does statistical inference refer to? (1 mark)
b) State and briefly explain three characteristics of a good estimate. (9 marks)
c) The Twilight Dental Association wants to taste which of the toothpaste brands is
better for fighting tooth decay. A random sample is taken of 21 persons using each
toothpaste. The average number of cavities for the first group over a 10 year period is
25 with a standard deviation of 5. In the second group, the average number of
cavities is 23 with a standard deviation of 4. Assuming that the distribution of
cavities is normal and of equal variance for all the users of toothpastes 1 and 2,
determine if any of the toothpaste brands is better for fighting tooth decay at 5% level
of significance. (10 marks)
Questions Four
a) State the central limit theorem. (2 marks)
b) i) What is the difference between binomial distribution and poison distribution?
(2 marks)
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ii) Under what conditions can the Poisson distribution be used as an
approximation to the binomial distribution? (3 marks)
c) A claim is made that the average income of a company is Ks 26, 500 with a standard
deviation of Ksh 8,750. A sample of 100 employees was picked and their mean
income found to be Ksh . 24,510. Questions were raised why a sample with a mean
of Ksh 24,510 would be found from a population with a mean income of Ksh 26,500.
Assess the likelihood of getting a sample mean as low or lower than Ksh 24,510 if the
population mean is indeed ksh 26,500. (7 marks)
d) The manager of a Television station must determine what percentage of households in
the city have more than one Television set. A random sample of 500 homes reveals
that 275 homes have two or more sets. What is the 90% confidence interval for the
proportion of all homes with two or more sets? Interpret your answer. (6 marks)
Question Five
a) The Table below gives the distribution of AEC 303 exam scores for a random sample
of 100 university students. Are the AEC 303 exam scores normally distributed at 5%
level of significance? (10 marks)
____________________________________
AEC 303 exam score No. of students
____________________________________
251 – 350 3
351 – 450 25
451 – 550 50
551 - 650 20
651 – 750 2
____________________________________
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b) The following table gives an hypothetical per capita income (Y) and the percentage of
economy represented by agriculture (X) reported by the Mwokihs research group for
2009 for 15 African countries.
____________________________________
Country Y X
____________________________________
Kenya 76 6
Tanzania 10 16
Mauritius 44 9
South Africa 47 8
Rwanda 23 14
Uganda 19 11
Nigeria 13 12
Botswana 19 10
Zambia 8 18
Zimbabwe 44 5
Ghana 4 26
Algeria 31 8
Liberia 24 8
Sudan 59 9
Morocco 37 5
____________________________________
Required
i) Find the regression equation for the per capita income and the percentage of
economy in agriculture. Interpret your results. (10 marks)
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