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Hand out z tables
Introduction to Statistics for the Social Sciences
SBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Spring 2015
Room 150 Harvill Building8:00 - 8:50 Mondays, Wednesdays & Fridays.
http://courses.eller.arizona.edu/mgmt/delaney/d15s_database_weekone_screenshot.xlsx
Labs continue next week
Schedule of readings
Before next exam (March 6th)
Please read chapters 5, 6, & 8 in Ha & Ha
Please read Chapters 10, 11, 12 and 14 in PlousChapter 10: The Representativeness HeuristicChapter 11: The Availability HeuristicChapter 12: Probability and RiskChapter 14: The Perception of Randomness
By the end of lecture today 2/27/15
Use this as your study guide
Connecting raw scores, and z scores to probability, proportion and area of curve
Percentiles
Approaches to probability: Empirical, Subjective and Classical
Homework due – Monday (March 2nd)
On class website: Please print and complete homework worksheet #11Approaches to probabilities &Interpreting probabilities using the normal curve
.
50 554444 - 50 4
= -1.5
55 - 50 4
= +1.25
z of 1.5 = area of .4332
.4332 +.3944 = .8276
z of 1.25 = area of .3944
50 55
55 - 50 4
= +1.25
.5000 - .3944 = .1056
1.25 = area of .3944
.3944
52 5552 - 50 4
= +.5
55 - 50 4
= +1.25
z of .5 = area of .1915
.3944 -.1915 = .2029
z of 1.25 = area of .3944
.3944.1915
.8276
.1056
.2029
.4332.3944
What is probability
1. Empirical probability: relative frequency approach
Number of observed outcomes
Number of observations
Probability of getting into an educational program
Number of people they let in
Number of applicants
Probability of getting a rotten apple
Number of rotten apples
Number of apples
5
100
5% chance of getting a rotten
apple
400
60066% chance of getting admitted
What is probability
1. Empirical probability: relative frequency approach
Number of observed outcomes
Number of observations
Probability of hitting the corvette
Number of carts that hit corvette
Number of carts rolled
182
200
91% chance of hitting a corvette
= .91
10% of people who buy a house with no pool
build one. What is the likelihood that Bob will?
“There is a 20% chance that a new stock offered in an
initial public offering (IPO) will reach or
exceed its target price on
the first day.”
“More than 30% of the results from
major search engines for the
keyword phrase “ring tone” are fake
pages created by spammers.”
2. Classic probability: a priori probabilities based on logicrather than on data or experience.
All options are equally likely (deductive rather than inductive).
Number of outcomes of specific event
Number of all possible events
In throwing a die what is the probability of getting a “2”
Number of sides with a 2
Number of sides
In tossing a coin what is probability of getting a tail
Number of sides with a 1
Number of sides
1
2
50% chance of getting a tail
1
616% chance of getting a two=
=
LotteryLikelihood get question right
on multiple choice test
Chosen at random to be team captain
3. Subjective probability: based on someone’s personal judgment (often an expert), and often used when empirical and classic approaches are not available.
There is a 5% chance that Verizon will merge with Sprint
Bob says he is 90% sure he could swim across the river
Likelihood that
company will invent new
type of battery
Likelihood get a ”B” in the class
60% chance that Patriots will play at Super Bowl
Approach Example
Empirical There is a 2 percent chance of twins in a randomly-chosen birth
Classical There is a 50 % probability of heads on a coin flip.
Subjective There is a 5% chance that Verizon will merge with Sprint
The probability of an event is the relative likelihood that the event will occur.
The probability of event A [denoted P(A)], must lie
within the interval from 0 to 1:
0 < P(A) < 1
If P(A) = 0, then the event cannot occur.
If P(A) = 1, then the event is certain to occur.
The probabilities of all simple events must sum to 1
For example, if the following number of purchases were made by
P(S) = P(E1) + P(E2) + … + P(En) = 1
credit card: 32%
debit card: 20%
cash: 35%
check: 13%
Sum = 100%
P(credit card) = .32
P(debit card) = .20
P(cash) = .35
P(check) = .13
Sum = 1.0
Probability
What is the complement of the probability of an eventThe probability of event A = P(A).The probability of the complement of the event A’ = P(A’)
• A’ is called “A prime”
Complement of A just means probability of “not A”• P(A) + P(A’) = 100%• P(A) = 100% - P(A’) • P(A’) = 100% - P(A)
Probability of getting into an educational program66% chance of “admitted”34% chance of “not admitted”
100% chance of admitted or not
5% chance of “rotten apple”
Probability ofgetting a rotten apple
95% chance of “not rotten apple”
100% chance of rotten or not
Two mutually exclusive characteristics: if the occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic
Two events are mutually exclusive if they cannot occur at the same time (i.e. they have no outcomes in common).
Two propositions that logically cannot both be true.
http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man
WarrantyNo
Warranty For example, a car repair is either covered by the
warranty (A) or not (B).
Events are collectively exhaustive if their union isthe entire sample space S.
Two mutually exclusive, collectively exhaustive events are dichotomous (or binary) events.
For example, a car repair is either covered by the
warranty (A) or not (B).
WarrantyNo
Warranty
Collectively Exhaustive Events