# CRIM 320 Lecture Notes - Lecture 4: Binomial Distribution, Statistical Significance, Sampling Distribution

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30 May 2013

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Crim 320 – week 4 – Distributions, the Normal Curve, and Hypothesis Testing

Housekeeping:

- Outline has been revised

- Office hours have been revised: please feel free to go to any or all

- All assignments will be handed in during lecture

- Must have both names, both std numbers, and tutorial in which it will be picked-up

Objectives

- Discuss the fundamentals of the binomial distribution

- Explain how sample size affects statistical significance

- Explain how hypothesis testing and testing and tests of statistical significance are related to the

standard normal distribution.

- Sample has stats

- When we can make inferences from sample |stats to a population| parameter, it’s significant if

it has an effect, real results

Hypothesis Testing

- Hypothesis testing is about evaluating sample results. It focuses on two closely related questions

- What can we say about a population based on the results observed in a sample?

- Are the sample results identical to the results we would observe from the entire

population?

The binomial distribution

- Is relevant for variables that can only have two possible outcomes

- Ex. For example, flipping a coin. Would expect % heads but might not

- How often would we get a result that differed from our expectation of five?

- A binomial distribution is a dist that can only have two possible outcomes

Ex: Flip a coin

Sampling dist – a distribution of all possible sample outcomes for a statistic

Standard error – the standard deviation of a sampling distribution

Ex: Recidivism

- First, select 10 parolees at random, and count number of times they “succeed” within five years

of release. Then, repeat this process 500 times.

- See graph. Add from “Number of Trials” colum: 66 + 24 + 4 _ 2 = 96/500= 19.2%

How Unusual?