Exam: Management Research Methods 1 (MRM1)
Friday 28 October 2016, 9:00-12:00 (3 hours)
Question 1 [12 points]
1a). [4] Mention two statistics that measure the spread of a sample distribution and explain why
it is useful to have two such measures rather than just one.
1b). [4] A researcher has a random sample of 40 observations of a Likert variable with five
categories (strongly disagree, disagree, neutral, agree, strongly agree). Now the researcher
considers to define the category numbers 1=strongly disagree, 2=disagree, 3=neutral, 4=agree,
5=strongly agree, and test whether the mean category number in the population is bigger than 3
by doing a one-sample t test based on the available sample. Would this be a valid t test? Explain.
1c). [4] What is the difference between two variables that have a strong negative correlation and
two variables that have a weak negative correlation? Make two scatters to show the difference
and briefly explain the difference (in one line).
Question 2 [22 points]
A production department uses a target value for the production of an employer, namely a
minimum of 56 finished products per day. In order to check whether this target value is realistic,
the manager has the following research question: is the median daily production level higher
than 56 finished products per day? For 15 randomly chosen workers the daily productions are
measured. See the observations and the SPSS output below, where the variable prod is the daily
production, and:
sqrtprod =
prod-40, lnprod =
ln(prod-40),invprod =
-1/ (prod-40), prod2 =
(prod-40) 2 ,
= =
prod3 (prod-40) 3
, prod4 (prod-40) 4
Observations of Production
42 44 50 52 53 54 54 55 55 56 57 58 59 59 60
, Descriptive Statistics
N Mean Std. Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error
prod 15 53.87 5.222 -1.205 .580 1.073 1.121
sqrtprod 15 3.6287 .86535 -1.714 .580 2.588 1.121
lnprod 15 2.5005 .63540 -2.203 .580 4.587 1.121
invprod 15 -.1079 .11901 -3.030 .580 9.433 1.121
prod2 15 217.7333 119.88355 -.315 .580 -.539 1.121
prod3 15 3586.2667 2489.35472 .282 .580 -.860 1.121
prod4 15 60821.7333 50562.33796 .666 .580 -.651 1.121
Valid N (listwise) 15
2a). [3] Find the first quartile of the daily production using Tukey’s method.
2b). [10] Suppose the manager wants to answer the research question by doing a one-sample t
test. Based on the given SPSS output, decide which variable is best suited to be used as the test
variable of the t test, and check whether using it will lead to a valid t test.
2c). [6] Suppose the manager would decide to test the research question by applying a one-
sample t test with prod2 as the test variable. Give the calculation of the t statistic for this case.
2d). [3] Use the box plot below to explain why the daily production has positive kurtosis in the
table with descriptive statistics.
Friday 28 October 2016, 9:00-12:00 (3 hours)
Question 1 [12 points]
1a). [4] Mention two statistics that measure the spread of a sample distribution and explain why
it is useful to have two such measures rather than just one.
1b). [4] A researcher has a random sample of 40 observations of a Likert variable with five
categories (strongly disagree, disagree, neutral, agree, strongly agree). Now the researcher
considers to define the category numbers 1=strongly disagree, 2=disagree, 3=neutral, 4=agree,
5=strongly agree, and test whether the mean category number in the population is bigger than 3
by doing a one-sample t test based on the available sample. Would this be a valid t test? Explain.
1c). [4] What is the difference between two variables that have a strong negative correlation and
two variables that have a weak negative correlation? Make two scatters to show the difference
and briefly explain the difference (in one line).
Question 2 [22 points]
A production department uses a target value for the production of an employer, namely a
minimum of 56 finished products per day. In order to check whether this target value is realistic,
the manager has the following research question: is the median daily production level higher
than 56 finished products per day? For 15 randomly chosen workers the daily productions are
measured. See the observations and the SPSS output below, where the variable prod is the daily
production, and:
sqrtprod =
prod-40, lnprod =
ln(prod-40),invprod =
-1/ (prod-40), prod2 =
(prod-40) 2 ,
= =
prod3 (prod-40) 3
, prod4 (prod-40) 4
Observations of Production
42 44 50 52 53 54 54 55 55 56 57 58 59 59 60
, Descriptive Statistics
N Mean Std. Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error
prod 15 53.87 5.222 -1.205 .580 1.073 1.121
sqrtprod 15 3.6287 .86535 -1.714 .580 2.588 1.121
lnprod 15 2.5005 .63540 -2.203 .580 4.587 1.121
invprod 15 -.1079 .11901 -3.030 .580 9.433 1.121
prod2 15 217.7333 119.88355 -.315 .580 -.539 1.121
prod3 15 3586.2667 2489.35472 .282 .580 -.860 1.121
prod4 15 60821.7333 50562.33796 .666 .580 -.651 1.121
Valid N (listwise) 15
2a). [3] Find the first quartile of the daily production using Tukey’s method.
2b). [10] Suppose the manager wants to answer the research question by doing a one-sample t
test. Based on the given SPSS output, decide which variable is best suited to be used as the test
variable of the t test, and check whether using it will lead to a valid t test.
2c). [6] Suppose the manager would decide to test the research question by applying a one-
sample t test with prod2 as the test variable. Give the calculation of the t statistic for this case.
2d). [3] Use the box plot below to explain why the daily production has positive kurtosis in the
table with descriptive statistics.
