MA251 Probability & Statistics
Chapter 1: Picturing Distributions with Graphs
Statistics
organize, picture,
summarize real
data
Overview
Descriptive
Numeric
Graphic
bar graphs
pie charts
time plots
histograms
stemplots
box plots
scatter plots
infer, gener
Warm-Up
1. These histograms show the distributions of
the ages of actresses and actors when the
won an Oscar for Best Actress/Actor.
a.
b.
How would you describe each distribution?
What conclusion(s) might you draw?
Warm-Up
2. What do these histograms sug
Teams by County
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Teams by County
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Practice
The following is a list of estimated Presidential IQs.
80 103 104 105 118 119 120 120 121
121 122 123 126 126 128 128
130 130 131 132 132 132 132 133 133 133 134 135 135 137 138 145 147 150
152 15
MA251 Probability & Statistics
Chapter 4: Scatterplots & Correlation
Dr. Soltys
Essential Questions
(Scatterplots) and how is one created?
What is a scatterplot
What is the difference between an
explanatory variable and a response
variable?
How do we inte
MA251 Probability & Statistics
Chapter 5: Regression
Topics
Linear regression
Least-squares regression line
Coefficient of determination
Residual plots
Outliers & influential observations
Warnings about correlation & regression
Extrapolation
Lurking varia
MA251 Probability & Statistics
Chapter 6: Two-Way Tables
Dr. Soltys
Chapter 6
Two-Way Tables
In chapters 4 and 5, we investigated
relationships between two quantitative
variables. In this chapter we are looking for
relationships between two categorical
va
Warm-Up
Suppose that a study is conducted to explore the connection
between calculator use and success on the 11th grade PA state
math test (PSSA). The researcher collects the following
information from a group of 5700 11th grade students
throughout the s
Warm-Up
9.33 Getting teachers to come to school.
Elementary schools in rural India are usually small, with a
single teacher. The teachers often fail to show up for work. Here is
an idea for improving attendance: give the teacher a digital
camera with a ta
Warm-Up
10.49 Random numbers.
Many random number generators allow users to specify the range
of the random numbers to be produced. Suppose that you specify
that the random number Y can take any value between 0 and 2.
Then the density curve of the outcomes
Example
Suppose that Etown claims the average SAT score for
incoming Freshman (i.e. class of 2015) is 1126.5 with a
standard deviation of 141.5. In order to test this claim,
we will take a random sample of 10 students from the
class of 2015 and see if the
MA251 Probability & Statistics
Chapter 8: Producing Data: Sampling
Topics
Population vs. Sample
Sample Design
Non-random Samples
Random Samples
Cautions about sample surveys
Inference about the population
Impact of technology
Population vs. Sample
o
Resea
11.37 Playing the numbers.
Warm-Up
The numbers racket is a well-entrenched illegal gambling
operation in most large cities. One version works as follows: you
choose one of the 1000 three-digit numbers 000 to 999 and pay
your local numbers runner a dollar
MA251 Probability & Statistics
Chapter 14: Introduction to Inference
Statistics
Descriptive
Numeric
Graphic
bar graphs
pie charts
time plots
histograms
dotplots
stemplots
box plots
scatter plots
Inferential
center
spread
mean
median
mode
range
IQR
stand.
Review
Suppose that cards are to be selected from a standard
deck of 52 without replacement. Calculate each of the
following.
13
a. P(a diamond and a spade) 13
= 13
=.0 6 4
52
b.
51
4
P(an Ace or a 2)
12
+ 4 5 2 = 2 13 =.15 4
52
11 5 1 = 11 2 2 1 =.0 5 0
Chapter 22
Two Categorical Variables: The Chi-Square
Test
In this chapter, we determine how to
assess a relationship between two
categorical variables.
1
Essential Ideas
q
q
Chi-square distributions
Expected Counts in two-way tables and
the chi-square tes
MA251 Probability & Statistics
Chapter 20: Comparing Two Proportions
Comparing Two Proportions
Often we want to compare the proportions of two populations.
For example, we may want to compare the proportion of
women who react favorably to a certain adver
MA251 Probability & Statistics
Test 3 Review
Quiz
Items
Chapter 14
The critical value, z*, used for constructing a 96% confidence
interval for a population mean is . . .
a.
b.
c.
d.
1.645
2.054
2.326
2.576
Chapter 14
A 99% confidence interval for the aver
MA251 Probability & Statistics
Test 1 Review
Take a look at . . .
6.19, 6.20, 6.22, 6.23, 6.24, 6.25, 6.28
On the exam you should be able to . . .
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Match a scatterplot to an r value.
Identify what effect a particular
MA251 Probability & Statistics
Test 2 Review
Quiz
Items
Chapter 10
Assume that event A occurs with probability .3 and event B occurs
with probability .4. Assume that A and B are disjoint events.
The probability that both events occur (A and B) is . . .
a.
MA251
Probability & Statistics
Final Review
Dr. Soltys
1. What are the mean and standard
deviation of the following distribution?
x
0
1
2
3
4
5
6
P(x)
.2
.15
.1
.25
.13
.09
.08
x =2.55
s =1.87
2. The test average of the 12 men in a class
is 78% while the
MA251: Probability & Statistics
Test 3 Formula Sheet
z *
Sample Size for Desired Margin of Error ( known): n
m
2
2
z*
Sample Size for Desired Margin of Error (proportion): n pq
m
Plus-4 Confidence Interval:
One-sample proportion: p
X 2
n4
Two-sam
An article titled Teen Boys Forget Whatever It Was
appeared in the Australian newspaper The Mercury. It
described a study of academic performance and attention
span and reported that in a random sample of 20 the mean
time to distraction for teenage boys w
MA251: Probability & Statistics
Final Exam Formula Sheet
Descriptive Statistics
Mean: x
x1 x2 x3
n
Position of Median =
xn
n 1
2
Standard Deviation:
xi
Standardized Scores: z score
2
n
or
s
xi
2
n 1
x
Correlation & Regression
Pearson Correlation
MA251: Probability & Statistics
Test 1 Formula Sheet
Mean: x =
x1 +x2 +x3 +L +xn
n
Position of Median =
(
Standard Deviation: s = xi - m )
n
Standardized Scores: z - score =
2
s=
( xi - m )
2
n-1
x- m
s
Pearson Correlation Coefficient: r =
- x yi - y
x
MA251: Probability & Statistics
Test 2 Formula Sheet
Discrete Random Variables
Mean of Discrete Random Variable: x xi pi
2
Variance of Discrete Random Variable: x ( xi i ) 2 pi
General Probability Rules
General Addition Rule: P( A or B) P( A) P( B) P( A &