Advanced Statistics Midterm Exam

Advanced
Statistics
Midterm
Exam
1.
The number of tourists coming to
Morocco
has surged in the last 5 years. A researcher wants to know
if
hotels
in the country’s two major tourist destinations,
Agadir and Marrakesh, are affected by this surge. He surveys a
sample of 1
6
hotels in Agadir and
21
hotels in Marrakesh
and asks them about their
occupancy rates in the month
of April. He found the following results.
City
Agadir
Marrakesh
n
16
21
Mean
occupancy rate
(
)
73
%
81
%
Sample Standard deviation (s)
8.2
%
1
1
.3%
From these results, does the researcher have enough evidence to conclude that occupancy rates in Marrakech and
Agadir are different (at 5% significance level)?
2.
A political
researcher
wants to compare the political participation amongst the youth in Rabat and Casablanca.
He interviews a sample of
7
5 young people (21
30) in Rabat and found that
31
of them vote in elections. He also
interviewed a sample of 1
04
young people in C
asablan
ca and found that only
36
of them vote
.
Does the researcher have enough evidence
, at
α=0.
05
significance level,
to conclude that political participation
amongst the youth is different in Rabat and
Casablanca?
3.
A marketing
expert
wants to compare the age variability of the
Moroccan
audiences of two popular TV
soap
operas: one Turkish and the other Mexican.
She
surveyed a
total sample of 2
8
0 women and found that
148
of
them are regular followers of the Turkish soap opera, and only
8
1
follow
the Mexican program
regularly
. The
women
who are regular followers
were then asked their ages and the results are as follow:
Soap Opera
Turkish
Mexican
Sample m
ean age of audience
44
3
6
Sample s
tandard deviation of age of audience
16.1
9.7
Using
α=0.05
, is
age
variability
significantly different between the audiences of the 2 soap operas?
4.
The National Transportation Safety Board
(NTSB)
publishes statistics on the number of automobile
crashes that
people in various age groups have.
According to these statistics
, young
people aged
18
24 had an accident rate of
14%, which is much higher than those for other age groups
.
A researcher
believes that
these
statistics are
exaggerated
since young drivers have become more careful.
He surveyed 56
young drivers
aged 18
24 and found
that
7
had an accident
this year
.
Can the researcher reject
NTSB
’s claim at
α=
0.05 significance level?
5.
According to the Moroccan Office National des Chemins de Fer (ONCF), the direct train between Casablanca
and Fez takes an average of 3 hours and 36 m
inutes to reach its destination, with a standard deviation of 12
.5
minutes
.
Recently, train schedules have been changed in Morocco and the ONCF wants to know if this has
affected the ability of its trains to be
consistent
in their arrival times
. It surveye
d a random sample of
2
8 trains
travelling from Casablanca to Fez and found that the standard deviation
is 17.25 minutes.
Is there enough evidence, at
α=
0.05 level of significance, to suggest that the
new scheduling ha
s
reduced
the
ability of the Casablanca
Fez train to be
consistent
?
error: