Exam (elaborations)
MRM tentamen
- Course
- Institution
Tentamen van 8 pagina's voor het vak Management Research Methods 1 aan de UvA (MRM1 tentamen)
[Show more]
Seller
Follow
Gebroedersruigrok
Reviews received
Content preview
Management Research Methods 1 (MRM1)Exam – Friday, 23 October – 17:00-20:00 – 3 hours
Question 1 – Quartiles and Transformation
A short research resulted in data of 20 household incomes (thousands of euros):
19.0 18.5 22.5 20.5 28.0 26.0 33.5 29.0 35.0 34.0
36.5 35.0 45.0 39.5 50.0 46.0 53.5 50.5 89.5 74.0
1a. (5) If we wanted to draw a box plot, then we would need to draw whiskers. What is the starting point
and endpoint of the upper whisker? Use Tukey's hinges.
First, put the data in ascending order:
1 2 3 4 5 6 7 8 9 10
18.5 19.0 20.5 22.5 26.0 28.0 29.0 33.5 34.0 35.0
11 12 13 14 15 16 17 18 19 20
35.0 36.5 39.5 45.0 46.0 50.0 50.5 53.5 74.0 89.5
1
𝐿𝐿1 = 2 ∙ (1 + 10) = 5.5 ⟹ 𝑄𝑄1 = 𝑋𝑋5 + 0.5 ∙ (𝑋𝑋6 − 𝑋𝑋5 ) = 27.0
1
𝐿𝐿3 = 2 ∙ (11 + 20) = 15.5 ⟹ 𝑄𝑄3 = 𝑋𝑋15 + 0.5 ∙ (𝑋𝑋16 − 𝑋𝑋15 ) = 48.0
The upper whisker starts at 𝑄𝑄3 = 48.0
𝐼𝐼𝐼𝐼𝐼𝐼 = 𝑄𝑄3 − 𝑄𝑄1 = 21.0 ⟹ 1.5 ∙ 𝐼𝐼𝐼𝐼𝐼𝐼 = 31.5
Upper fence: 𝑄𝑄3 + 1.5 ∙ 𝐼𝐼𝐼𝐼𝐼𝐼 = 79.5
Therefore, there is one outlier: 89.5 > 79.5 and the upper whisker ends at 74.0
1b. (3) Researchers in financial statistics often use 'median household income' instead of 'mean household
income'. Why?
The income distribution is skewed to the right, and the mean is sensitive to the extremely high
incomes, while the median is not. So using median, rather than mean income, results in a more
accurate picture of the general income level, as it will not be affected by abnormalities at the
extreme end.
MRM1 – 1
, As the SPSS-table below shows, the Income distribution is quite skewed. In order to perform a test, the
data have been transformed by using: 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 = ln(𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼).
Descriptive Statistics
N Mean Std. Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error
Income 20 39.275 18.123 1.381 0.512 2.159 0.992
LnIncome 20 3.581 0.427 0.314 0.512 -0.174 0.992
1c. (10) Is the population median of household income lower than € 40 000? This research question about
the median could be tested with a significance level of 5%. But first, motivate in detail (include
relevant statistical tests!) why it is better to test the median of Income, instead of the mean.
Motivation for test of the median and not the mean:
The sample size is small, so for a valid test of the population mean, the test variable must be normally
distributed.
However, the distribution of Income has servere positive skewness, as its skewness is 1.381 > 1.0.
Test Income for skewness: 𝑧𝑧 = 1.381/0.512 = 2.70, 𝑃𝑃(𝑧𝑧 < 2.70) = 0.9965, p-value = 2(1 − 0.9965) =
0.007 < 0.10, so the variable Income is significantly skewed. Therefore we cannot do a valid test of the
population mean.
LnIncome has no severe skewness: 0.314 < 1.0. Test LnIncome for skewness: 𝑧𝑧 = 0.314/0.512 = 0.61,
𝑃𝑃(𝑧𝑧 < 0.61) = 0.7291, p-value= 2�1– 0.7291� = 0.5418 > 0.10, so LnIncome is not significantly skewed.
Therefore we can do a valid test of the population mean of LnIncome. This corresponds with testing the
median of Income.
1d. (6) We could do the test whether the population median of household income is lower than € 40 000.
We will only do parts of the test: Give the hypotheses, calculate the test statistic t and interpret its
value.
Hypotheses:
H0: PMIncome = 40 H1: PMIncome < 40
H0: µSqrtIncome = ln(40) = 3.689 H1: µSqrtIncome < ln(40) = 3.689
Test statistic:
𝑥𝑥̅ − 𝜇𝜇 3.581 − 3.689
𝑡𝑡 = 𝑠𝑠 ~𝑡𝑡[𝑑𝑑𝑑𝑑 = 𝑛𝑛 − 1 = 19] 𝑡𝑡 = = −1.131
0.427
√𝑛𝑛 √20
Interpretation: The mean difference in the sample lies 1.131 standard errors below the value given in the
null-hypothesis.
MRM1 – 2
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 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 these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Gebroedersruigrok. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.21. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
53340 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now