Hand out z tables

Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2015 Room 150 Harvill Building 8:00 - 8:50 Mondays, Wednesdays & Fridays.

Labs continue next week

Schedule of readings Before next exam (March 6 th ) Please read chapters 5, 6, & 8 in Ha & Ha Please read Chapters 10, 11, 12 and 14 in Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 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 2 nd ) On class website: Please print and complete homework worksheet #11 Approaches to probabilities &Interpreting probabilities using the normal curve

= = z of 1.5 = area of =.8276 z of 1.25 = area of = = = area of = = z of.5 = area of =.2029 z of 1.25 = area of

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 % chance of getting a rotten apple % 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 % 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 logic rather 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 % chance of getting a tail % chance of getting a two = = Lottery Likelihood 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(E 1 ) + P(E 2 ) + … + P(E n ) = 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 event The 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 program 66% chance of “admitted” 34% chance of “not admitted” 100% chance of admitted or not 5% chance of “rotten apple” Probability of getting 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 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. No Warranty For example, a car repair is either covered by the warranty (A) or not (B).

Events are collectively exhaustive if their union is the entire sample space S. Events are collectively exhaustive if their union is the entire sample space S. Two mutually exclusive, collectively exhaustive events are dichotomous (or binary) events. 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). Warranty No Warranty Collectively Exhaustive Events