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程序代写案例-ECON1007W1
时间：2021-05-14
UNIVERSITY OF SOUTHAMPTON ECON1007W1
______________________________________________________
SEMESTER 2 EXAMINATIONS 2016-17
TITLE Statistics for Economics
DURATION 120 MINS (2 Hours)
______________________________________________________
This paper contains 5 questions
Answer FOUR questions.
An outline marking scheme is shown in brackets to the right of each question.
A Set of Statistical Tables is provided with this examination paper.
The tables are labelled ‘Statistical Tables (including DD123 and MM123) For Use in
Examinations’.
Only University approved calculators may be used.
A foreign language direct ‘Word to Word’ translation dictionary (paper version) ONLY
is permitted. Provided it contains no notes, additions or annotations.
Page 1 of 5 + Appendices (Statistical Tables)
Copyright 2017 v01 © University of Southampton Page 1 of 5
2 ECON1007W1
1. Students at New College can either do a degree in ‘arts’ or a degree in
‘economics’. Students are classified as being ‘home’ students (i.e UK residents)
or ‘overseas’ students. The web site of the university gives the following
information: “Home students make up 61% of the student population. 30% of
students are studying for an arts degree. Overseas students account for 37%
of the arts students. Of the economists, 43% are from overseas.” (All the
percentage have been rounded to the nearest integer)
A professor of the economics department realizes that one of the figures in the
web-page must be wrong and, after talking to the school office, he finds that
the percentage of home students is in fact 59%.
a) Explain why a percentage of 61% of home students was wrong. [5]
b) Using the correct figure of 59% of home students, find the probability that a
home student will be studying economics. [5]
c) Three students decide (independently) to move from arts to economics.
There were originally 60 people studying arts. What is the probability that the
students who have changed course do not all come from the same region?
(Hint: You may want to calculate the probability that the three students all come
from the same region. Recall that there are two regions: UK and overseas). [5]
d) Suppose that all 3 students that move to economics do come from the same
region. A person is chosen at random from the economists. What is the
probability that this person is a home student? [5]
e) Suppose that the 3 students that moved to economics are overseas
students. 5 students are chosen at random from “arts”. What is the probability
that 3 will be from oversees? [5]
2. A drug company produces pills containing an active ingredient. Assume that
the mean weight of the active ingredient is 30 milligrams per pill and the
variance (in squared milligrams) is 1.5. For quality assurance, a random sample
of 30 pills is selected.
Copyright 2017 v01 © University of Southampton Page 2 of 5
3 ECON1007W1
a) What is the probability that the sample mean is exactly 30 milligrams?
Explain your answer [5]
b) What is the probability that the sample mean will be less than 29.5
milligrams? [5]
c) Explain whether the result above relies on the use of the Central Limit
Theorem. [5]
d) Assume now that the population distribution is normal. How likely that a
sample variance of 2.05 or higher would be found if the population variance
is 1.5? [5]
e) Determine the upper limit of the sample variance such that the probability
of exceeding this limit is 5%? [5]
3. The University of Southampton IT service has found that on average 6% of
the computers on campus need to be repaired each month. Assume that there
are 100 computers on campus.
a) What is the probability that exactly 3 computers will break down this month?
[5]
b) Use the Poisson approximation to the binomial distribution to estimate the
probability that at least 2 computers will stop working this month [5]
c) Instead of a Poisson, can you use another distribution to approximate the
binomial? Explain your answer [5]
d) Assume now that the number of computer failures during a month has a
Poisson distribution with mean 1. A computer has just failed. Find the
probability that at least 15 days will elapse before there is a further computer
failure (you can assume that a month is made of 30 days). [5]
e) Suppose that 15 days has already passed since the last failure. What is the
probability that at least 15 days will elapse before there is another computer
failure. [5]
TURN OVER
Copyright 2017 v01 © University of Southampton Page 3 of 5
4 ECON1007W1
4. A regression model takes the following form:
= + 11 + 22 + 11 + 22+
where the errors are normally distributed. The least square estimates based
on a dataset of 25 observations, together with the associated standard errors,
are given below.
Coefficient
Standard
Error
Intercept 0.315 0.338
X1 0.049 0.023
X2 -0.036 0.022
Z1 0.206 0.183
Z2 0.048 0.209
Regression Statistics
Adjusted R Square 0.636027664
F 3.679636867
Observations 25
a) Test the null hypothesis that the coefficient 1 = 0 versus the alternative
hypothesis of 1 ≠ 0 at the 10% significance level. [5]
b) What is the p-value of the least-square estimate ̂1 ? [5]
c) Construct a 95% confidence interval for 2. [5]
d) Test the overall significance of the regression model at the 5% level. [5]
e) A researcher wonders whether the model would be improved by removing
Z1 and Z2. What are null and alternative hypotheses which are appropriate for
this case? [5]
5. a) What is the difference between an estimator and an estimate? Explain
your answer fully. [5]
Copyright 2017 v01 © University of Southampton Page 4 of 5
5 ECON1007W1
b) Explain whether the estimator
n
x is an unbiased and consistent estimator
of the population mean µ [5]
c) What is the sampling distribution of the sample mean? [5]
d) What are Type I and Type II errors in statistical hypothesis testing?
Explain your answer. [5]
e) Explain what the relationship is between the cumulative distribution
function and the probability density function. [5]
END OF PAPER
Copyright 2017 v01 © University of Southampton Page 5 of 5
Social Sciences
Examination Feedback
2016/2017
Module Code & Title: Econ1007 – Statistics for Economics
Module Coordinator: Carmine Ornaghi
Mean Exam Score: 59.2
Percentage distribution across class marks:
UG Modules
1 st (70% +) 30
2.1 (60-69%) 33
2.2 (50-59%) 19
3rd (40-49%) 7
Fail (25-39%) 6
Uncompensatable Fail
(<25%)
5
PGT Modules
70% +
60-69%
50-59%
<50%
Overall strengths of candidates’ answers:
Students answered questions related to regression analysis and hypothesis testing with relative
ease. Q3 and Q5 were the most favoured questions and had the highest scoring.
Overall weaknesses of candidates’ answers:
Overall students struggled in answering questions related to probability distributions and questions
related to the normal distribution. Q1 and Q2 were the least scoring questions.
Pattern of question choice:
The exam required students to answer 4 out of 5 questions. Q5 was the most commonly
attempted, followed by Q1 and Q3. Q4 was the least attempted question.
Issues that arose with particular questions:
Students did not seem comfortable tackling questions regarding probabilities. The mistakes they
made were very similar, indicating that they did not grasp the essence of the given question.
Further comments not covered above:
Overall the students did well, with a large proportion of students getting an average above 60 per
cent. However, those who could not do well struggled across all questions.
Discipline vetting completed By (Name): Zacharias Maniadis Date:19/06/2017
学霸联盟
______________________________________________________
SEMESTER 2 EXAMINATIONS 2016-17
TITLE Statistics for Economics
DURATION 120 MINS (2 Hours)
______________________________________________________
This paper contains 5 questions
Answer FOUR questions.
An outline marking scheme is shown in brackets to the right of each question.
A Set of Statistical Tables is provided with this examination paper.
The tables are labelled ‘Statistical Tables (including DD123 and MM123) For Use in
Examinations’.
Only University approved calculators may be used.
A foreign language direct ‘Word to Word’ translation dictionary (paper version) ONLY
is permitted. Provided it contains no notes, additions or annotations.
Page 1 of 5 + Appendices (Statistical Tables)
Copyright 2017 v01 © University of Southampton Page 1 of 5
2 ECON1007W1
1. Students at New College can either do a degree in ‘arts’ or a degree in
‘economics’. Students are classified as being ‘home’ students (i.e UK residents)
or ‘overseas’ students. The web site of the university gives the following
information: “Home students make up 61% of the student population. 30% of
students are studying for an arts degree. Overseas students account for 37%
of the arts students. Of the economists, 43% are from overseas.” (All the
percentage have been rounded to the nearest integer)
A professor of the economics department realizes that one of the figures in the
web-page must be wrong and, after talking to the school office, he finds that
the percentage of home students is in fact 59%.
a) Explain why a percentage of 61% of home students was wrong. [5]
b) Using the correct figure of 59% of home students, find the probability that a
home student will be studying economics. [5]
c) Three students decide (independently) to move from arts to economics.
There were originally 60 people studying arts. What is the probability that the
students who have changed course do not all come from the same region?
(Hint: You may want to calculate the probability that the three students all come
from the same region. Recall that there are two regions: UK and overseas). [5]
d) Suppose that all 3 students that move to economics do come from the same
region. A person is chosen at random from the economists. What is the
probability that this person is a home student? [5]
e) Suppose that the 3 students that moved to economics are overseas
students. 5 students are chosen at random from “arts”. What is the probability
that 3 will be from oversees? [5]
2. A drug company produces pills containing an active ingredient. Assume that
the mean weight of the active ingredient is 30 milligrams per pill and the
variance (in squared milligrams) is 1.5. For quality assurance, a random sample
of 30 pills is selected.
Copyright 2017 v01 © University of Southampton Page 2 of 5
3 ECON1007W1
a) What is the probability that the sample mean is exactly 30 milligrams?
Explain your answer [5]
b) What is the probability that the sample mean will be less than 29.5
milligrams? [5]
c) Explain whether the result above relies on the use of the Central Limit
Theorem. [5]
d) Assume now that the population distribution is normal. How likely that a
sample variance of 2.05 or higher would be found if the population variance
is 1.5? [5]
e) Determine the upper limit of the sample variance such that the probability
of exceeding this limit is 5%? [5]
3. The University of Southampton IT service has found that on average 6% of
the computers on campus need to be repaired each month. Assume that there
are 100 computers on campus.
a) What is the probability that exactly 3 computers will break down this month?
[5]
b) Use the Poisson approximation to the binomial distribution to estimate the
probability that at least 2 computers will stop working this month [5]
c) Instead of a Poisson, can you use another distribution to approximate the
binomial? Explain your answer [5]
d) Assume now that the number of computer failures during a month has a
Poisson distribution with mean 1. A computer has just failed. Find the
probability that at least 15 days will elapse before there is a further computer
failure (you can assume that a month is made of 30 days). [5]
e) Suppose that 15 days has already passed since the last failure. What is the
probability that at least 15 days will elapse before there is another computer
failure. [5]
TURN OVER
Copyright 2017 v01 © University of Southampton Page 3 of 5
4 ECON1007W1
4. A regression model takes the following form:
= + 11 + 22 + 11 + 22+
where the errors are normally distributed. The least square estimates based
on a dataset of 25 observations, together with the associated standard errors,
are given below.
Coefficient
Standard
Error
Intercept 0.315 0.338
X1 0.049 0.023
X2 -0.036 0.022
Z1 0.206 0.183
Z2 0.048 0.209
Regression Statistics
Adjusted R Square 0.636027664
F 3.679636867
Observations 25
a) Test the null hypothesis that the coefficient 1 = 0 versus the alternative
hypothesis of 1 ≠ 0 at the 10% significance level. [5]
b) What is the p-value of the least-square estimate ̂1 ? [5]
c) Construct a 95% confidence interval for 2. [5]
d) Test the overall significance of the regression model at the 5% level. [5]
e) A researcher wonders whether the model would be improved by removing
Z1 and Z2. What are null and alternative hypotheses which are appropriate for
this case? [5]
5. a) What is the difference between an estimator and an estimate? Explain
your answer fully. [5]
Copyright 2017 v01 © University of Southampton Page 4 of 5
5 ECON1007W1
b) Explain whether the estimator
n
x is an unbiased and consistent estimator
of the population mean µ [5]
c) What is the sampling distribution of the sample mean? [5]
d) What are Type I and Type II errors in statistical hypothesis testing?
Explain your answer. [5]
e) Explain what the relationship is between the cumulative distribution
function and the probability density function. [5]
END OF PAPER
Copyright 2017 v01 © University of Southampton Page 5 of 5
Social Sciences
Examination Feedback
2016/2017
Module Code & Title: Econ1007 – Statistics for Economics
Module Coordinator: Carmine Ornaghi
Mean Exam Score: 59.2
Percentage distribution across class marks:
UG Modules
1 st (70% +) 30
2.1 (60-69%) 33
2.2 (50-59%) 19
3rd (40-49%) 7
Fail (25-39%) 6
Uncompensatable Fail
(<25%)
5
PGT Modules
70% +
60-69%
50-59%
<50%
Overall strengths of candidates’ answers:
Students answered questions related to regression analysis and hypothesis testing with relative
ease. Q3 and Q5 were the most favoured questions and had the highest scoring.
Overall weaknesses of candidates’ answers:
Overall students struggled in answering questions related to probability distributions and questions
related to the normal distribution. Q1 and Q2 were the least scoring questions.
Pattern of question choice:
The exam required students to answer 4 out of 5 questions. Q5 was the most commonly
attempted, followed by Q1 and Q3. Q4 was the least attempted question.
Issues that arose with particular questions:
Students did not seem comfortable tackling questions regarding probabilities. The mistakes they
made were very similar, indicating that they did not grasp the essence of the given question.
Further comments not covered above:
Overall the students did well, with a large proportion of students getting an average above 60 per
cent. However, those who could not do well struggled across all questions.
Discipline vetting completed By (Name): Zacharias Maniadis Date:19/06/2017
学霸联盟
