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