Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Fall 2013
Practice Questions Units 5 and 6 Chapter 6 and Chapter 7 (7.1 to 7.4)
1.
Approximately how many observations do we need to draw in a simple random sample so that the
width of a 90% confidence interval is no more than 0.4 units long? (Assume the population
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Fall 2013
Stats 2035 Midterm #2 Booklet Solutions
A. Exponential
Example 1. Jobs are sent to a printer at an average of 3 jobs per hour.
y= # of jobs sent to the printer per hour y=0,1,2,.
~
3
x=time between jobs at the printer in hours x>0
~
3
E(
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Spring 2016
What is Statistics?
Statistics is the science of collecting,
organizing, summarizing and interpreting
numerical facts, which we call data
Statistics start with a question
1.
What percent of students at UWO
smoke?
2. Are there differences in the number of
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Spring 2016
Other Graphical Displays
1. Frequency Polygon
same horizontal axis as histogram
constructed by marking a point at the
midpoint of each class
height of graph is equal to the
frequency of that class
these points are then connected with
straight lines
p
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Spring 2016
Chapter 4 Probability
(The study of randomness)
Most statistical analysis begins by collecting
data
the best way to collect data is to set up an
experiment and observe the results
however, before you run your experiment,
you are not sure what will be th
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Spring 2016
Measuring The Spread/Measures of
Variability (section 3.2)
Example
We are to compare four factories that are
producing 600ml bottles of water. We need
to determine which factory is doing the best
job. We take a sample of 5 bottles of water
from a selecte
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Spring 2016
Chapter 3 Descriptive Statistics
In addition to graphing the data, we can gain
more insight by condensing the data into a
few single numbers which will summarize
the distribution in a clear and concise
manner
these single numbers are called statistics
t
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Spring 2016
Grouped Data (section 3.3)
(I) Weighted Means (not in textbook)
In calculating the mean of a population or
sample, we sum each measurement and
divide by the number of measurements
that is, each measurement is given the
same importance or weight
But somet
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Spring 2016
(Skip Counting Rules (Section 4.3) for now)
Conditional Probability and Independent
Events (sections 4.6/4.7)
Sometimes probabilities need to be
reevaluated as additional information
becomes available.
Example 4.6
Suppose in example 4.1, someone has
inspe
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Spring 2016
Bayes Rule (section 4.8)
Sometimes you need to determine posterior
probabilities based on your prior
probabilities
That is, you may want to determine P(AB)
given that you know P(A) and P(BA).
P(AB) =
P( A B)
P( B)
=
P ( A) P ( B  A)
P( B)
The above is
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Fall 2013
Statistics 2035  Midterm Exam #1  Formula Sheet
Descriptive Statistics
Group all of the n data into K classes, where K is the smallest whole number,
To find the position of pth percentile, you need to calculate the index
2K n
i = n(p /100)
BoxandWhisk
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Fall 2013
Statistical Sciences 2035 201213
MID TERM EXAM #1
Friday, November 16, 2012
7:00 pm  9:30 pm
Read these instructions
1. This is a 2.5 hours closed book examination. Nonprogrammable calculators are
permitted.
2. There are 36 multiple choice questions. 1
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Fall 2013
Statistical Sciences 2035 201112
MID TERM EXAM #1
Friday, November 16, 2012
7:00 pm  9:00 pm
Read these instructions
1. This is a closed book examination. Calculators are permitted.
2. There are 30 multiple choice questions. 1 mark for each correct answ
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Fall 2013
Practice Test on Chapters 4 and 5
Use the following information for the next TWO questions:
The number of hits on a website follows a Poisson distribution with an average rate of 3.3 per minute,
while the time between hits follows an exponential distribut
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Fall 2013
Units 7 and 8  Practice Problems Chapter 7 (7.5 to 7.8), Chapter 8, Chapter 9
1.
Mr. Chips produces potato chips and packages the chips in 200g bags. A consumer believes that the
bags may contain less than 200g on average. Suppose that the standard devia
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Fall 2013
Solutions to Unit 78 Practice Test
1. Answer A
Type I error = P(reject Ho  Ho is true). Thus they are accusing Mr. Chips of
underfilling bags when in fact Mr Chips is filling the bags to the correct limit
2. Answer B
t* = 126.05 110 = 1.865; From ttabl
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2035

Spring 2016
Chapter 5 Discrete Random Variables and
Probability Distributions
Definition
A random variable is a variable which
assigns a numerical value to every outcome
of a random experiment
There are two types of random variables:
discrete and continuous
1. Discre