Probability and Statistics for Business Applications
70 207

Fall 2014
Introduction to Accounting (70122): Midterm #2
Business Stat 70207
NAME:
_
SECTION:
_
Instructions
Time Allowed: 50 minutes. A nongraphing calculator is allowed but not necessary. Please read the instructions
for each question very carefully and write
Probability and Statistics for Business Applications
70 207

Summer 2015
Examining a Distribution Shape
Graphs can help determine:
1.
2.
Symmetric or skewed
Modes (local peaks of a distribution)
Unimodal  one peak
Bimodal  two peaks
Symmetry: Shapes of Distributions

Symmetric histogram in which the right half is a mirror i
Probability and Statistics for Business Applications
70 207

Summer 2015
Facts about leastsquares regression
If we reverse the roles of the explanatory and response
variables, we will get a different regression line
The slope, b1 is related to the correlation coefficient, r
The leastsquares line passes through the means of t
Probability and Statistics for Business Applications
70 207

Summer 2015
Individual vs. Variable  Question 1
Airport administrators take a sample of airline baggage
and record the number of bags that weigh more than 75
pounds. What is the case?
1)
2)
3)
4)
The weight of each bag.
Average weight of the bags.
Each piece of bagg
Probability and Statistics for Business Applications
70 207

Summer 2015
Questions
Can we determine the mean from a boxplot?
What is IQR?
No!
IQR = Q3  Q1
One criteria considers points below Q11.5(IQR)
or above Q3+1.5(IQR) as outliers
Can we show outliers differently in boxplots?
Yes, there is a boxplot variant that does thi
Probability and Statistics for Business Applications
70 207

Summer 2015
(70)207
Practice Final Exam
Summer 2015
On the actual exam you will have 75 minutes.
1. (1 point each) For each of (a)(l), choose the most appropriate distribution (family) from this
list:
Bernoulli
Binomial
Poisson
Geometric
Uniform
Exponential
N
Probability and Statistics for Business Applications
70 207

Summer 2015
Measure of direction: Covariance
 Direction +
Not Strength
1
Covariance and Correlation
Spread
(One Variable)
Not intuitive
Variance
(Unit^2
)
Relationshi
p
(Two
Variables)
Covarian
(Unitdependent)
ce
Easier to understand!
Standard
Deviatio
n (Unit
)
C
Probability and Statistics for Business Applications
70 207

Summer 2015
PrinciplesofExperimentalDesign
Three big ideas of experimental design:
Control the effects of confounding variables on the response,
simply by comparing two or more treatments.
Randomize use impersonal chance to assign subjects to
treatments.
Replicate
Probability and Statistics for Business Applications
70 207

Summer 2015
Conditional Distribution
Does parental smoking influence the smoking habits of
their high school children?
Summary twoway
table: High school
students were asked
whether they smoke
and whether their
parents smoke.
1
Simpsons paradox
An association or comp
Probability and Statistics for Business Applications
70 207

Summer 2015
Mean and Median
Median is the point that divides the area in half
Mean is the balanced point at which the curve
would balance
Pop Quiz Question?
In which of these cases are the mean and the median the same?
(a)
(b) Skewed to the left
Symmetric
(c) Skewed
Probability and Statistics for Business Applications
70 207

Summer 2015
Review
Data Analysis: describing data using graphs and numerical
summaries
Goal: describing the most important features of data
Plot your data: stem plot,
Histogram
Interpret what you see:
Shape, Center, Spread,
Outliers
Normal
Distribution?
1
Data
Densit
Probability and Statistics for Business Applications
70 207

Summer 2015
Example
Question 1
A
B
Question 2
Conditional Probability
Example
Roll a die.
A = outcome is even, B = outcome is 3 or more.
What is P(AB)? What is P(BA)?
Customers of a fastfood chain restaurant.
80% use mustard, 75% use ketchup, and 70% use both.
Wha
Probability and Statistics for Business Applications
70 207

Summer 2015
Variability of a statistic
The variability of a statistic is described by the spread of its
sampling distribution, usually in the form of a margin of
error.
We will learn how to calculate it later this semester
Example: In the proportion of soda cans exam
Probability and Statistics for Business Applications
70 207

Summer 2015
Properties of independent random variables
If are independent then:
=0
=0
=
If and have a linear dependence then 0
However, it could happen that without
being independent.
Bernoulli trial
Random variable means:
With
probability
(success)
With probabi
Probability and Statistics for Business Applications
70 207

Summer 2015
Example: Car Recyclers, Inc
can buy cars at government auctions, $2,000 each
Car is good with prob. 0.75 and can be resold for
$3,000
Car is bad with prob. 0.25 and can be resold for $400
Car Recyclers, Inc. buys a set of 6 cars
What is the probabilit
Probability and Statistics for Business Applications
70 207

Summer 2015
Bayes Theorem Example 1
Automobile sales incentive
10% of people who come to showroom buy a car.
Idea: Oer a free dinner.
After six months nd:
40% of people who purchased a car accepted a free dinner.
10% of people who did not purchase a car accepted.
Que
Probability and Statistics for Business Applications
70 207

Summer 2015
Example
Multiple random variables
Independence of random variables
Covariance
Correlation
Covariance and Correlation:
Properties of the expected value, variance,
covariance
Summary: Rules for means and
variances
If X is a random variable and a and b are f
Probability and Statistics for Business Applications
70 207

Summer 2015
Geometric Random Variable
Geometric Probability Distribution
Trading Card (Coupon) Collecting
Trading Card (Coupon) Collecting
Geometric Spacing Between
Occurrences
Continuous Random Variable
Random variable that can take any numerical value in an interva
Probability and Statistics for Business Applications
70 207

Summer 2015
Example
A gas station has a 1000gallon tank that is lled in the
morning.
Previous experience indicates that any demand from 0 to 1000
gallons per day is equally likely
In this case the density function is
Cumulative Distribution
Assume is a random va
Probability and Statistics for Business Applications
70 207

Summer 2015
Example
Example
Independence
Two events are independent if the probability that one event
occurs on any given trial of an experiment is not affected or
changed by the occurrence of the other event.
Disjoint events are not independent.
If A and B are disjo
Probability and Statistics for Business Applications
70 207

Summer 2015
Reasoning of Significance Tests
We have seen that the properties of the sampling distribution of the sample mean help
us estimate a range of likely values for population mean .
We can also rely on the properties of the sample distribution to test hypothes
Probability and Statistics for Business Applications
70 207

Summer 2015
Where Have We Been and Where are We
Going?
Know how to summarize data with graphs, statistics, and
verbal descriptions i.e. Descriptive Statistics
Discuss data collection methods
Understand that results will vary from sample to sample (or
experiment to ex
Probability and Statistics for Business Applications
70 207

Summer 2015
Topics 3
Inference
Estimating with Confidence
Test of the Significance
(Additional reading: Chapter 6 in text book)
1
Overview of Inference
Methods for drawing conclusions about a population from
sample data are called statistical inference
Methods
Con
Probability and Statistics for Business Applications
70 207

Summer 2015
Review
Relationship between two variables
Plot your data
Scatterplot
Interpret what you see
Direction, Form, Strength, outliers?
Mathematical model?
Regression line?
Producing Data
Designing Experiments
Toward Inference
(Additional reading: Chapter 3 in t
Probability and Statistics for Business Applications
70 207

Fall 2012
36(70)  207  Final Review
By Jessi Cisewski
Fall 2012
Chapter 1: Examining Distributions
1.1 Displaying distributions with graphs
1.2 Describing distributions with numbers
1.3 Density curves and the normal distribution
Chapter 2: Examining Relationshi
Probability and Statistics for Business Applications
70 207

Fall 2012
36 (70)  207 Formula Sheet
Sample standard deviation:
n
i=1 (xi
x)2
n1
s=
Correlation:
r=
1
n1
n
i=1
(xi x) (yi y )
sx
sy
Leastsquares regression line:
y = b0 + b1 x,
b1 = r
sy
,
sx
b0 = y b1 x
Residuals:
residual = y y
Mean and variance of a discrete