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.
1b. (3) Researchers in financial statistics often use 'median household income' instead of 'mean household
income'. Why?
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.
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.
Question 2 – Distributions
Sketches don't have to be very precise drawings, but they do clearly contain the properties that are typical
for the case in question, sometimes with exaggeration, or clearly not contain properties that are not
typical.
2a. (2) Draw a sketch of a box plot, associated with a distribution with negative skew.
2b. (2) Draw a sketch of a box plot, associated with a distribution with negative kurtosis.
2c. (2) Draw one sketch containing both distributions: 𝑍𝑍~𝑁𝑁(0, 1) and 𝑇𝑇~𝑡𝑡[𝑑𝑑𝑑𝑑 = 8]. Clearly denote which
is which. They may overlap.
MRM1 – 1
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.
1b. (3) Researchers in financial statistics often use 'median household income' instead of 'mean household
income'. Why?
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.
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.
Question 2 – Distributions
Sketches don't have to be very precise drawings, but they do clearly contain the properties that are typical
for the case in question, sometimes with exaggeration, or clearly not contain properties that are not
typical.
2a. (2) Draw a sketch of a box plot, associated with a distribution with negative skew.
2b. (2) Draw a sketch of a box plot, associated with a distribution with negative kurtosis.
2c. (2) Draw one sketch containing both distributions: 𝑍𝑍~𝑁𝑁(0, 1) and 𝑇𝑇~𝑡𝑡[𝑑𝑑𝑑𝑑 = 8]. Clearly denote which
is which. They may overlap.
MRM1 – 1
