Exam study book Mathematical Statistics for Economics and Business of Ron C. Mittelhammer (Chapter 1 to chapter 5) - ISBN: 9781461450221 (First stats test)
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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller mtonxazanele21. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R183,00. You're not tied to anything after your purchase.
