UNIVERSITY OF TORONTO SCARBOROUGH
Department of Computer and Mathematical Sciences
March 16, 2018
MIDTERM TEST
STAB22H3 Statistics I
Duration: 1 hour 45 minutes
Last Name: First Name:
Student number:
Aids allowed:
- One handwritten letter-sized sheet (both sides) of notes prepared by you
- Non-programmable, non-communicating calculator
Standard Normal, t and the binomial distribution tables are attached at the end.
This test is based on multiple-choice questions. There are 35 questions. All questions carry
equal weight. On the Scantron answer sheet, ensure that you enter your last name, first
name (as much of it as fits), and student number (in “Identification”).
Mark in each case the best answer out of the alternatives given (which means the nu-
merically closest answer if the answer is a number and the answer you obtained
is not given.)
Also before you begin, complete the signature sheet, but sign it only when the invigilator
collects it. The signature sheet shows that you were present at the exam.
There are 24 pages including this page and statistical tables. Please check to see that you
have all the pages.
Good luck!!
ExamVersion: A
1
,1. The normal quantile plot for a data set is shown below:
Based on this information, which of the following statements regarding the distribution
of this data is/are true?
I The mean of this data set is greater than its median.
II The median of this data set is greater than its mean.
III For this data set, the distance between the first quartile and the median is less
than that between the third quartile and the median.
(a) Only I is true.
(b) Only II is true.
(c) Only III is true.
(d) Only I and III are true.
(e) None of the three statements is true.
Solution:
(d)
This is the characteristics shape of quantile plot of a right skewed distribution
and I and III are properties of right-skewed distributions.
2
,2. A researcher finds a correlation of 0.4 between personal income and the number of
years of college completed. Based upon this finding he can conclude that
(a) a person who attended four years of college will have an annual income of
$40,000.
(b) more years of education causes higher income.
(c) personal income is a right skewed variable.
(d) more years of education are associated with higher income.
(e) personal income is normally distributed.
Solution: d
3. A StatCrunch output gave the following five-number summary for scores on a statistics
exam :
29.00, 55.75, 66.50, 72.50, 99.00.
There were 104 students in this class and all of them wrote this exam. The grades
were all integers (i.e. no decimal grades were given in this exam). How many students
had grades between 55.75 and 66.5? (Note that this actually means between 56 and
66, including 56 and 66).
(a) 4
(b) 13
(c) 26
(d) 52
(e) none of the above
Solution:
c
This just the proportion of students between Q1 and the median. Grades being
integers, imply that they cannot be at exactly at Q1 and med because they are
decimals in this data set. That is 25% of 104 = 26.
3
, 4. The lifespans of gorillas in a particular zoo are normally distributed with mean 16
years and standard deviation 1.7 years.
Use the 68-95-99.7 rule to estimate the proportion of gorillas in this zoo living longer
than 12.6 years.
(a) 2.5%
(b) 5%
(c) 16%
(d) 95%
(e) 97.5%
Solution:
12.4 is 2 standard deviations away from the mean and we want the proportion
to the right, which is 100% − 2.5% = 97.5%.
5. The following side-by-side bar chart shows the acceptance status (accepted or rejected)
and gender of students’ applications to graduate school.
Approximately what percent of males are rejected?
(a) Approximately 20%
(b) Approximately 30%
(c) Approximately 40%
(d) Approximately 50%
(e) Approximately 60%
Solution:
200
200+500
= 29%, i.e. approxiatel 30%
4
Department of Computer and Mathematical Sciences
March 16, 2018
MIDTERM TEST
STAB22H3 Statistics I
Duration: 1 hour 45 minutes
Last Name: First Name:
Student number:
Aids allowed:
- One handwritten letter-sized sheet (both sides) of notes prepared by you
- Non-programmable, non-communicating calculator
Standard Normal, t and the binomial distribution tables are attached at the end.
This test is based on multiple-choice questions. There are 35 questions. All questions carry
equal weight. On the Scantron answer sheet, ensure that you enter your last name, first
name (as much of it as fits), and student number (in “Identification”).
Mark in each case the best answer out of the alternatives given (which means the nu-
merically closest answer if the answer is a number and the answer you obtained
is not given.)
Also before you begin, complete the signature sheet, but sign it only when the invigilator
collects it. The signature sheet shows that you were present at the exam.
There are 24 pages including this page and statistical tables. Please check to see that you
have all the pages.
Good luck!!
ExamVersion: A
1
,1. The normal quantile plot for a data set is shown below:
Based on this information, which of the following statements regarding the distribution
of this data is/are true?
I The mean of this data set is greater than its median.
II The median of this data set is greater than its mean.
III For this data set, the distance between the first quartile and the median is less
than that between the third quartile and the median.
(a) Only I is true.
(b) Only II is true.
(c) Only III is true.
(d) Only I and III are true.
(e) None of the three statements is true.
Solution:
(d)
This is the characteristics shape of quantile plot of a right skewed distribution
and I and III are properties of right-skewed distributions.
2
,2. A researcher finds a correlation of 0.4 between personal income and the number of
years of college completed. Based upon this finding he can conclude that
(a) a person who attended four years of college will have an annual income of
$40,000.
(b) more years of education causes higher income.
(c) personal income is a right skewed variable.
(d) more years of education are associated with higher income.
(e) personal income is normally distributed.
Solution: d
3. A StatCrunch output gave the following five-number summary for scores on a statistics
exam :
29.00, 55.75, 66.50, 72.50, 99.00.
There were 104 students in this class and all of them wrote this exam. The grades
were all integers (i.e. no decimal grades were given in this exam). How many students
had grades between 55.75 and 66.5? (Note that this actually means between 56 and
66, including 56 and 66).
(a) 4
(b) 13
(c) 26
(d) 52
(e) none of the above
Solution:
c
This just the proportion of students between Q1 and the median. Grades being
integers, imply that they cannot be at exactly at Q1 and med because they are
decimals in this data set. That is 25% of 104 = 26.
3
, 4. The lifespans of gorillas in a particular zoo are normally distributed with mean 16
years and standard deviation 1.7 years.
Use the 68-95-99.7 rule to estimate the proportion of gorillas in this zoo living longer
than 12.6 years.
(a) 2.5%
(b) 5%
(c) 16%
(d) 95%
(e) 97.5%
Solution:
12.4 is 2 standard deviations away from the mean and we want the proportion
to the right, which is 100% − 2.5% = 97.5%.
5. The following side-by-side bar chart shows the acceptance status (accepted or rejected)
and gender of students’ applications to graduate school.
Approximately what percent of males are rejected?
(a) Approximately 20%
(b) Approximately 30%
(c) Approximately 40%
(d) Approximately 50%
(e) Approximately 60%
Solution:
200
200+500
= 29%, i.e. approxiatel 30%
4
