EC1007
All Candidates
January Examinations 2015
DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE
CHIEF INVIGILATOR
Department
Economics
Module Code
EC1007
Module Title
Statistics for Economists I
Exam Duration
Two hours
(in words)
CHECK YOU HAVE THE CORRECT QUESTION PAPER
Number of Pages
3
Number of Questions
5
Instructions to
Candidates
Answer ALL questions
For this exam you are allowed to use the following
Calculators
Yes
Books/Statutes
No
Additional Stationery
Yes
Version 1
The approved calculator (that is Casio FX-83ES or Casio FX-85ES) may
be used
Not required
Economics Stats Tables (Kmietowicz and Yannoulis) Green/Black
cover
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EC1007
All Candidates
1. The following table shows the weekly earnings (in pounds) of a random sample of 12 workers from a city
in the UK.
213
345
609
273
167
243
444
524
199
682
325
274
With this information:
a. Calculate the sample mean, variance and standard deviation.
[5%]
b. Obtain the median and the first and third quartile for this sample. What is the economic
interpretation of the quartiles and the median in this case?
[5%]
c. It is found that the coefficient of skewness is equal to 0.8593. What can you say about the shape
of the distribution of the data? Give an economic interpretation of the shape in this case.
[5%]
2. Answer the following questions without using a Venn diagram:
a. The owner of a bookshop is interested in the profile of customers purchasing nonfiction books.
She finds that 49% of all the buyers decide to buy at least one nonfiction book. Also, 17% of those
who buy a nonfiction book are under 30 years old. She also finds that 13% of all her customers
are less than 30 years old.
i. What is the probability that a randomly chosen customer buys a nonfiction book and is
under 30?
[5%]
ii. What is the probability that a customer who is not under 30 does not purchase a
nonfiction book?
[10%]
b. It is known that 96% of the workers in a factory are contributing to the pension scheme provided
by the company. Of all contributors, 75% of them are aged more than 55 years, and only 15% of
those who are not contributing to the pension scheme are aged more than 55 years. What is the
probability that a worker randomly chosen among those aged more than 55 years has contracted
the pension?
[10%]
3. The manager of an estate agency knows from past experience that the maximum number of houses sold
during a week will never be higher than five. The probability distribution of the number of houses sold
during a week is shown in the following table:
Houses sold
0
1
2
3
4
5
Probability
0.17
0.28
0.30
0.15
0.06
0.04
a. What is the expected number of houses sold in a week for this agency?
[10%]
b. What is the probability that the agency sells at least 3 houses?
[5%]
4. Let Z denote a random variable that follows a standard normal distribution
𝑍~𝑁(0,1)
And let X denote a random variable that follows a normal distribution with mean 56 and variance 900:
𝑋~𝑁(56,900)
Find the following probabilities showing all steps [5% each]:
a. P(Z<1.24)
b. P(-0.25<Z<2.30)
c. P(X>47)
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EC1007
All Candidates
5. As part of the quality control of the production process in a factory producing tyres, a random sample of
20 items is taken to be analysed. Historically, the (population) mean weight of the tyres produced is 26 lbs
with a (population) standard deviation of 0.75 lbs. The weight of the tyres is assumed to be normally
distributed.
a. What is the probability that the mean of the sample taken is less than 26.5 lbs?
[10%]
b. Knowing that the mean weight of the tyres in the sample is 26.3 lbs, construct and interpret the
95% confidence interval for the population mean, µ.
[10%]
c. Assume now that the population parameters of the distribution are unknown, and that the
standard deviation of the weight of the tyres in the sample is 1.25 lbs. Construct and interpret the
99% confidence interval for the mean in this case.
[10%]
END OF PAPER
Version 1
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