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First test of statistics
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Exam study book Mathematical Statistics for Economics and Business of Ron C. Mittelhammer (Chapter 1 to chapter 5) - ISBN: 9781461450221 (First stats test)
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Class notes ENGLISH Mathematical Statistics for Economics and Business
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First test of statistics
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UNIVERSITY OF THE FREE STATEBLOEMFONTEIN CAMPUS
EECM3724
STATISTICS FOR ECONOMICS
DEPARTMENT OF ECONOMICS AND FINANCE
TEST: FIRST TEST
MARKS: 50 & TIME: 120 MINUTES
This test paper consists of 3 questions on 3 pages. This test counts 40% of your module mark. A formulae
sheet and 4 statistical tables (for the cumulative z-distribution, and for the right-tailed t-, chi-squared and F-
distribution) accompanies this paper. The Afrikaans paper is on the reverse.
INSTRUCTIONS
1) Answer all the questions. Number your answers clearly!
2) Write legibly, using only black or blue ink. Do not write in the margins of your answer sheet.
3) Show all your work/calculations.
4) Where necessary, round final answers to the nearest FOUR decimals (except when this yields
unsatisfactory results).
2
a. Use fractions (e.g. 3) and radicals (e.g. √2) for greater accuracy.
b. Use scientific notation (e.g. 0.000067 = 6.7 × 10−5 ) for answers very close to zero.
QUESTION 1 [14]
1.1) The table below contains data about the share of food spending in total spending (in percentage points,
𝑓𝑜𝑜𝑑𝑠ℎ𝑎𝑟𝑒) and monthly per capita household income (𝑖𝑛𝑐𝑜𝑚𝑒) for a random sample of nine Free State
households.
Household A B C D E F G H I
𝑓𝑜𝑜𝑑𝑠ℎ𝑎𝑟𝑒 49 49 35 26 42 21 47 48 53
𝑖𝑛𝑐𝑜𝑚𝑒 3361 3831 4145 4980 4162 6309 3216 4135 3223
1.1a) Estimate the sample means and sample standard deviations of 𝑓𝑜𝑜𝑑𝑠ℎ𝑎𝑟𝑒 and 𝑖𝑛𝑐𝑜𝑚𝑒 for these 9
Free State households. [3]
1.1b) Write down the interquartile range (IQR) for 𝑖𝑛𝑐𝑜𝑚𝑒. [3]
1.1c) Report the largest z-score (in absolute terms) for 𝑓𝑜𝑜𝑑𝑠ℎ𝑎𝑟𝑒. Are there any outliers present? Briefly
explain. [2]
1.1d) Estimate the sample correlation coefficient between 𝑓𝑜𝑜𝑑𝑠ℎ𝑎𝑟𝑒 and 𝑖𝑛𝑐𝑜𝑚𝑒. Comment on the
direction and strength of the estimated relationship. [4]
1.2) The mean monthly rental rate of a two-bedroom flat in Bloemfontein is R3000, with a variance of
462400. Use Chebychev’s rule to find the interval that contains at least 60.94% of the monthly rental rates
of two-bedroom flats in Bloemfontein. [2]
1
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