# Chapter 1 - ECMT1020 Chapter 1 Hypothesis Testing I...

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Chapter 1: Hypothesis Testing 1 1 ECMT1020 Chapter 1 Hypothesis Testing I Hypothesis Testing I Extracted from “Australian Business Statistics” Modified by Dr Boris Choy for ECMT1020

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Chapter 1: Hypothesis Testing 1 2 ! Topics covered 1. Binomial Distribution 2. Normal Approximation to Binomial Distribution 3. Hypothesis Testing for a Population Proportion ! References Black 5.3, 6.3 and 9.4
Chapter 1: Hypothesis Testing 1 3 Learning Objectives Learning Objectives ! Identify the type of situations that can be described by the binomial distribution. ! Understand the approximation of the normal distribution (a continuous distribution) to the binomial distribution (a discrete distribution). ! Perform hypothesis testing on the population proportion of the binomial distribution.

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Chapter 1: Hypothesis Testing 1 4 Binomial Distribution Binomial Distribution Assumptions of the binomial distribution: ! Experiment involves n identical trials, where n is fixed before the trials are conducted. ! Each trial has exactly two possible outcomes: success and failure ! Each trial is independent of the previous trials Definitions: p is the probability of a success on any one trial q = 1-p is the probability of a failure on any one trial p and q are constant throughout the experiment X is the number of successes in the n trials: p = X / n (relative frequency probability) p and n are known as the parameters of a binomial distribution
Chapter 1: Hypothesis Testing 1 5 Binomial Distribution Binomial Distribution ! Let X is the number of successes out of n trials. ! The probability distribution of X is given by ! P( X = x ) is the probability of observing x successes given n and p . ! X has a binomial Bin( n , p ) distribution, we write X~Bin( n , p ) ! The mean of X is E[ X ]= np ! The variance of X is Var[ X ] = npq )! ( ! ! where ,..., 2 , 1 , 0 , )( x n x n x n n x q p x n x X P x n x - = ! ! " # \$ \$ % & = ! ! " # \$ \$ % & == -

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Chapter 1: Hypothesis Testing 1 6 Properties of Properties of B B inomial inomial D D istribution istribution ! The binomial distribution is symmetric if p = 0.5 ! It is positively (right) skewed if p < 0.5 ! It is negatively (left) skewed if p > 0.5 ! Its skewness decreases as n increases ! It is considered to be symmetric if np > 5, nq > 5 and n 30
Chapter 1: Hypothesis Testing 1 7 Binomial Distribution: Demonstration Problem 5.3 Binomial Distribution: Demonstration Problem 5.3 ! According to the New Zealand Department of Labour, approximately 4% of all workers in Auckland are unemployed. What is the probability of selecting two or fewer unemployed workers in a sample of twenty?

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Chapter 1 - ECMT1020 Chapter 1 Hypothesis Testing I...

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