Name: ___________________________________________________________ Nº: _________
Statistics II
Master in Management
Nova School of Business and Economics
EXAM - MODEL
XX December 2015, XX
Duration: 1h30
INSTRUCTIONS
Turn off your mobile phone!
Authorized Material: Pen, calculating machine and this assignment.
Write your name and student number on the first page of this assignment.
This assignment must always be stapled.
The answers to the questions should be written in the locations indicated in this
assignment.
You can use the back of each sheet as a draft.
Any situation of plagiarism (such as the use of unauthorized material and/or
communication with colleagues) will have as immediate consequence a drop out in
the course this semester.
You are not allowed to ask questions during the EXAM.
Before starting the EXAM confirm that this assignment has 21 pages numbered 1 to
21.
At the end of this assignment you will find included some key equations and
statistical tables.
You must remain seated in your place by the end of the EXAM.
When the time expires please turn your EXAM over and wait for its collection made
by invigilators.
Nova School of Business and Economics 1
,Name: ___________________________________________________________ Nº: _________
About the EXAM
A Portuguese couple with 3 kids, needs to buy an apartment, quickly. They need a big
enough apartment where all the members can fit. However they are not sure where to
search for: in Lisbon or in Linha do Estoril, depending on the Price (thousands of €),
Areas (sq. meters), View, Typology… on the 21st October they decided to hire a
Portuguese research team from NovaSBE: Vera, Diogo and Pedro as they have shown
to have experience on this area. Next day, the team, with the help of a real estate agent,
selected from their database, at random 50 apartments in the 2 locations. This was done
in order to be able to assume that each of the observed/measured variables is
representative of the respective statistical population. Data was organized, partially
processed and several questions and doubts were analyzed in a meeting that started at 9
am on the 23rd October.
Today we are here, all together, in order to produce information to help the couple in
their decision =)
For each question in Groups I to III indicate only one answer in the table on page 9
Each correct answer is worth 0,70 values
Each wrong answer is worth 0.10 negative (-0.10).
Each answer blank or poorly marked is worth 0.
Group I
The Areas (X, m2) are different if you pick up apartments in Lisbon (center) or in
Linha do Estoril… was one of the first comments of the team.
The sample provided the following indicators:
50
1 50
x i 6500
i 1
(x i x) 2 400
49 i1
1. The standard deviation and the standard error of the mean are aprox.
a) 400 and 130
b) 400 and 20
c) 20 and 2,83
d) None of the others
Nova School of Business and Economics 2
, Name: ___________________________________________________________ Nº: _________
2. “I think we can state that the mean area of an apartment, despite the location
(Lisbon or Linha do Estoril), is at least 140 m2!” Pedro stated during the
meeting. “I do not know but I suspect that you are wrong! If you use a 95%
confidence level…” Vera commented. In order to find out who is right we
should
a) perform a Hypothesis test considering Ho:µ=140 vs H1: µ≠140
b) perform a Hypothesis test considering Ho:µ≤140 vs H1: µ>140
c) perform a Hypothesis test considering Ho:µ≥140 vs H1: µ<140
d) compute a confidence interval for the mean area (µ)
3. 10 minutes after the meeting has started Diogo, looking at the sample
indicators and some additional information about the distribution of the area,
said “a test was performed in order to find out if we can consider the area as
being Normally distributed and unfortunately p=0,0065 so we are in trouble
and cannot compute confidence intervals for the mean area!” This is
a) not true and the lower limit (with a 95% confidence level) is 125,4 m2
b) true because we cannot state that X ~ N
c) not true and the upper limit (with a 95% confidence level) is 135,5 m2
d) not true because we can state that X ~ N
4. “Let’s perform a test: Ho: µ=140 vs H1: µ≠140” Vera, as always very wise,
suggested “… using a 95% confidence level”. The difference between the two
critical values is … and the p-value is …
a) >9 / < 0,05
b) <9 / < 0,05
c) <9 / > 0,05
d) >9 / > 0,05
5. “What if we had performed a one-sided test instead of a two-sided (refer to
4.) with H1: µ<140, would our previous decision change (with the same
confidence level) ?” asked Pedro…
a) I do not have enough information
b) No
c) Yes
d) none of the others
Nova School of Business and Economics 3
Statistics II
Master in Management
Nova School of Business and Economics
EXAM - MODEL
XX December 2015, XX
Duration: 1h30
INSTRUCTIONS
Turn off your mobile phone!
Authorized Material: Pen, calculating machine and this assignment.
Write your name and student number on the first page of this assignment.
This assignment must always be stapled.
The answers to the questions should be written in the locations indicated in this
assignment.
You can use the back of each sheet as a draft.
Any situation of plagiarism (such as the use of unauthorized material and/or
communication with colleagues) will have as immediate consequence a drop out in
the course this semester.
You are not allowed to ask questions during the EXAM.
Before starting the EXAM confirm that this assignment has 21 pages numbered 1 to
21.
At the end of this assignment you will find included some key equations and
statistical tables.
You must remain seated in your place by the end of the EXAM.
When the time expires please turn your EXAM over and wait for its collection made
by invigilators.
Nova School of Business and Economics 1
,Name: ___________________________________________________________ Nº: _________
About the EXAM
A Portuguese couple with 3 kids, needs to buy an apartment, quickly. They need a big
enough apartment where all the members can fit. However they are not sure where to
search for: in Lisbon or in Linha do Estoril, depending on the Price (thousands of €),
Areas (sq. meters), View, Typology… on the 21st October they decided to hire a
Portuguese research team from NovaSBE: Vera, Diogo and Pedro as they have shown
to have experience on this area. Next day, the team, with the help of a real estate agent,
selected from their database, at random 50 apartments in the 2 locations. This was done
in order to be able to assume that each of the observed/measured variables is
representative of the respective statistical population. Data was organized, partially
processed and several questions and doubts were analyzed in a meeting that started at 9
am on the 23rd October.
Today we are here, all together, in order to produce information to help the couple in
their decision =)
For each question in Groups I to III indicate only one answer in the table on page 9
Each correct answer is worth 0,70 values
Each wrong answer is worth 0.10 negative (-0.10).
Each answer blank or poorly marked is worth 0.
Group I
The Areas (X, m2) are different if you pick up apartments in Lisbon (center) or in
Linha do Estoril… was one of the first comments of the team.
The sample provided the following indicators:
50
1 50
x i 6500
i 1
(x i x) 2 400
49 i1
1. The standard deviation and the standard error of the mean are aprox.
a) 400 and 130
b) 400 and 20
c) 20 and 2,83
d) None of the others
Nova School of Business and Economics 2
, Name: ___________________________________________________________ Nº: _________
2. “I think we can state that the mean area of an apartment, despite the location
(Lisbon or Linha do Estoril), is at least 140 m2!” Pedro stated during the
meeting. “I do not know but I suspect that you are wrong! If you use a 95%
confidence level…” Vera commented. In order to find out who is right we
should
a) perform a Hypothesis test considering Ho:µ=140 vs H1: µ≠140
b) perform a Hypothesis test considering Ho:µ≤140 vs H1: µ>140
c) perform a Hypothesis test considering Ho:µ≥140 vs H1: µ<140
d) compute a confidence interval for the mean area (µ)
3. 10 minutes after the meeting has started Diogo, looking at the sample
indicators and some additional information about the distribution of the area,
said “a test was performed in order to find out if we can consider the area as
being Normally distributed and unfortunately p=0,0065 so we are in trouble
and cannot compute confidence intervals for the mean area!” This is
a) not true and the lower limit (with a 95% confidence level) is 125,4 m2
b) true because we cannot state that X ~ N
c) not true and the upper limit (with a 95% confidence level) is 135,5 m2
d) not true because we can state that X ~ N
4. “Let’s perform a test: Ho: µ=140 vs H1: µ≠140” Vera, as always very wise,
suggested “… using a 95% confidence level”. The difference between the two
critical values is … and the p-value is …
a) >9 / < 0,05
b) <9 / < 0,05
c) <9 / > 0,05
d) >9 / > 0,05
5. “What if we had performed a one-sided test instead of a two-sided (refer to
4.) with H1: µ<140, would our previous decision change (with the same
confidence level) ?” asked Pedro…
a) I do not have enough information
b) No
c) Yes
d) none of the others
Nova School of Business and Economics 3
