THE UNIVERSITY OF THE WEST INDIES
EXAMINATIONS OF DECEMBER 2018
Code and Name of Course: ECON 1005 – INTRODUCTION TO STATISTICS
Paper:
Date and Time:
Duration: 2 hours
INSTRUCTIONS TO CANDIDATES: This paper has 6 pages and 4 questions.
Candidates are required to answer ALL Questions.
Silent Cordless Non Programmable Calculators may be used.
The University of the West Indies
Course Code: ECON 1005
2018/…./…..
DO NOT WRITE ON THE BACK OF THIS SHEET: USE ONE SIDE ONLY
INSTRUCTIONS: Each page must be signed by the Examiners and where applicable, the University Examiner and/or the External
Examiner. Where the examination does not require a University Examiner, the form must be signed by the First and Second
Examiners. Completed forms should be handed to the Assistant Registrar (Examinations). The EXTERNAL EXAMINER is
requested to sign the question paper and return it with comments, if any, (on a separate sheet) , to the Assistant Registrar
(Examinations).
………………………………………..
First Examiner
……………………………………………..
University Examiner
………………………………………..
Second Examiner
……………………………………………..
External Examiner (where applicable)
Date: 2018……/……/…
Date: 2018……/……/……
Page 2
ANSWER ALL QUESTIONS
1. A research company was hired by a local car dealership to investigate the carbon dioxide (CO2)
emissions of imported CNG vehicles. A stratified random sample of CNG vehicles was hence
taken from the dealership using country of origin as the stratification factor. The data collected,
which focused on the grams of CO2 emitted per km, were entered on a Minitab spreadsheet for
analysis. Exhibit I below was subsequently generated.
Exhibit I
Country
N
Mean
Median
Tri. Mean
Std. Dev.
S.E. Mean
Germany
35
121
129
120
*
2.48
Japan
38
115
113
105
17.6
**
South Korea
25
108
103
116
15.2
3.04
a) Determine the values of * and **.
[2]
b) Identify the biased point estimator(s) and point estimate(s) for the average CO2 emissions per
km of all German CNG vehicles.
[2]
c) Give both a point estimator and point estimate for the variance of CO2 emissions per km of all
South Korean CNG vehicles.
[2]
d) Assuming normality, find the probability that the CO2 emissions per km of Japanese CNG
vehicles will be above 150 grams.
[4]
e) Assuming normality, construct and interpret a 98% confidence interval for the average CO2
emissions per km of all South Korean CNG vehicles.
[6]
f) An article recently published in an automotive magazine claimed that the emissions from all
German CNG vehicles were on average below 110 grams of CO2 per km. You are required to
test at the 5% level of significance the validity of this claim.
The University of the West Indies
Course Code: ECON 1005
2018/..../...../
DO NOT WRITE ON THE BACK OF THIS SHEET: USE ONE SIDE ONLY
INSTRUCTIONS: Each page must be signed by the Examiners and where applicable, the University Examiner and/or the External
Examiner. Where the examination does not require a University Examiner, the form must be signed by the First and Second
Examiners. Completed forms should be handed to the Assistant Registrar (Examinations). The EXTERNAL EXAMINER is
requested to sign the question paper and return it with comments, if any, (on a separate sheet) , to the Assistant Registrar
(Examinations).
………………………………………..
First Examiner
……………………………………………..
University Examiner
………………………………………..
Second Examiner
……………………………………………..
External Examiner (where applicable)
Date: 2018……/……/…
Date: 2018……/……/……
Page 3
Complete the following:
i.
Give the null and alternative hypothesis of this test.
[2]
ii.
Determine the critical value(s) of this test.
[2]
iii.
Compute the value of the test statistic.
[2]
iv.
State the decision rule.
[1]
v.
Give your decision based on the available sample evidence.
[1]
vi.
Hence, state your conclusion.
[2]
2. Complete the following:
a) A Jamaican tour guide company offers daily island tours of up to 15 persons per party to both
tourists and local residents. If 70% of their customers are typically tourists and a full party has
signed up for today’s tour:
i.
Name the random variable present in this problem and state its distribution.
[2]
ii.
What is the probability that 6 of the customers will be tourists?
[3]
iii.
Write an expression for the probability that at most 4 of the customers will be local
residents.
[4]
b) A service station has the capacity to service up to 5 cars at any given time with the number of
cars serviced per hour averaging 3. Write an expression for the probability that in the next hour
cars will have to be turned away.
[6]
c) The random variable Y is given by the following expression:
𝑌=
10𝑋 + 3
2
Where the random variable X is known to be normally distributed with a mean of 6 and
standard deviation of 7.
i.
What is the distribution of Y? Give a reason for your answer.
ii.
Determine the expected value of Y.
[3]
iii.
Determine the variance of Y.
[3]
The University of the West Indies
[2]
Course Code: ECON 1005
2018/..../...../
DO NOT WRITE ON THE BACK OF THIS SHEET: USE ONE SIDE ONLY
INSTRUCTIONS: Each page must be signed by the Examiners and where applicable, the University Examiner and/or the External
Examiner. Where the examination does not require a University Examiner, the form must be signed by the First and Second
Examiners. Completed forms should be handed to the Assistant Registrar (Examinations). The EXTERNAL EXAMINER is
requested to sign the question paper and return it with comments, if any, (on a separate sheet) , to the Assistant Registrar
(Examinations).
………………………………………..
First Examiner
……………………………………………..
University Examiner
………………………………………..
Second Examiner
……………………………………………..
External Examiner (where applicable)
Date: 2018……/……/…
Date: 2018……/……/……
Page 4
3. Complete the following:
a) A random sample of residents from various income brackets were asked their opinion on tax
reform for the country of Guyana. The data so gathered were analyzed by a statistician and the
results he obtained using MINITAB are shown below:
Expected counts are printed below observed counts
Low
26
(30.67)
60
(69.33)
34
(20)
*
For
Against
Neutral
Total
Chi-sq =
0.71 +
11.17 +
11.12 +
*** +
3.66 +
11.89 +
9.8 +
0.33 +
5.25 =
Middle
High
Total
75
(51.11)
95
(115.56)
30
(33.33)
200
14
(33.22)
105
(**)
11
(21.67)
130
115
260
75
450
55.2
DF = ??, p-value = ???
i.
Carefully define the null and alternative hypotheses of the 𝜒 2 test underlying the
generation of the above table.
[2]
ii.
Find the missing values ‘*’, ‘**’, ‘***’, ‘??’ and ‘???’.
[8]
iii.
What is the conclusion of this test? Give reasons for your answer.
[2]
b) A statistics students used the information from Exhibit 1 above and was able to generate the
following output from MINITAB:
Exhibit II
TWO SAMPLE Z FOR GERMANY VS JAPAN
Country
N
Mean
Median
Tri. Mean
Std. Dev.
S.E. Mean
Germany
35
121
129
120
*
2.48
Japan
38
115
113
105
17.6
**
95 PCT CI FOR MU GERMANY VS MU JAPAN: (-1.15, 13.15)
ZTEST MU JAPAN = MU SOUTH KOREA VS NE: Z = 1.64 p-value = ****
The University of the West Indies
Course Code: ECON 1005
2018/..../...../
DO NOT WRITE ON THE BACK OF THIS SHEET: USE ONE SIDE ONLY
INSTRUCTIONS: Each page must be signed by the Examiners and where applicable, the University Examiner and/or the External
Examiner. Where the examination does not require a University Examiner, the form must be signed by the First and Second
Examiners. Completed forms should be handed to the Assistant Registrar (Examinations). The EXTERNAL EXAMINER is
requested to sign the question paper and return it with comments, if any, (on a separate sheet) , to the Assistant Registrar
(Examinations).
………………………………………..
First Examiner
……………………………………………..
University Examiner
………………………………………..
Second Examiner
……………………………………………..
External Examiner (where applicable)
Date: 2018……/……/…
Date: 2018……/……/……
Page 5
i.
What is the student testing?
[2]
ii.
At what level of significance is this test being conducted?
[1]
iii.
Fill in the blank ‘****’.
[2]
iv.
Hence, state and justify the conclusion the student should draw.
[3]
4. A researcher interested in explaining the level of foreign reserves for the country of Trinidad
and Tobago estimated the following multiple regression model using yearly data spanning the
period 2001 to 2016:
𝐹𝑅 = 𝜶 + 𝜷𝑂𝐼𝐿 + 𝜸𝐸𝑋𝑃 + 𝜹𝐹𝐷𝐼
Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total
exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was
processed using MINITAB and the following is an extract of the output obtained:
The regression equation is *****
Predictor
Coef
StDev
t-ratio
p-value
Constant
5491.38
2508.81
2.1888
0.0491
OIL
85.39
18.46
4.626
0.0006
EXP
-377.08
112.19
*
0.0057
FDI
-396.99
160.66
-2.471
**
S = 2.45
R-sq = 96.3%
R-sq(adj) = 95.3%
Analysis of Variance
Source
DF
SS
MS
F
p
Regression
3
1991.31
663.77
?
??
Error
12
77.4
6.45
Total
15
a) Write out the regression equation.
[2]
b) Fill in the missing values ‘*’, ‘**’, ‘?’ and ‘??’.
[6]
The University of the West Indies
Course Code: ECON 1005
2018/..../...../
DO NOT WRITE ON THE BACK OF THIS SHEET: USE ONE SIDE ONLY
INSTRUCTIONS: Each page must be signed by the Examiners and where applicable, the University Examiner and/or the External
Examiner. Where the examination does not require a University Examiner, the form must be signed by the First and Second
Examiners. Completed forms should be handed to the Assistant Registrar (Examinations). The EXTERNAL EXAMINER is
requested to sign the question paper and return it with comments, if any, (on a separate sheet) , to the Assistant Registrar
(Examinations).
………………………………………..
First Examiner
……………………………………………..
University Examiner
………………………………………..
Second Examiner
……………………………………………..
External Examiner (where applicable)
Date: 2018……/……/…
Date: 2018……/……/……
Page 6
c) Hence test whether 𝜹 (the coefficient of FDI) is significant. Give reasons for your answer.
[4]
d) Perform the F Test making sure to state the null and alternative hypothesis.
[4]
e) Given an interpretation of the term “R-sq” and comment on its value.
[3]
f) Would you recommend the use of this model to predict the foreign reserves of Trinidad and
Tobago? Give reasons for your answer.
[3]
END OF QUESTION PAPER
The University of the West Indies
Course Code: ECON 1005
2018/..../...../
DO NOT WRITE ON THE BACK OF THIS SHEET: USE ONE SIDE ONLY
INSTRUCTIONS: Each page must be signed by the Examiners and where applicable, the University Examiner and/or the External
Examiner. Where the examination does not require a University Examiner, the form must be signed by the First and Second
Examiners. Completed forms should be handed to the Assistant Registrar (Examinations). The EXTERNAL EXAMINER is
requested to sign the question paper and return it with comments, if any, (on a separate sheet) , to the Assistant Registrar
(Examinations).
………………………………………..
First Examiner
……………………………………………..
University Examiner
………………………………………..
Second Examiner
……………………………………………..
External Examiner (where applicable)
Date: 2018……/……/…
Date: 2018……/……/……