# MGEB12H3 Study Guide - Midterm Guide: Null Hypothesis, Statistical Hypothesis Testing, Statistical Parameter

by OC81277

Department

Economics for Management StudiesCourse Code

MGEB12H3Professor

Victor YuStudy Guide

MidtermThis

**preview**shows pages 1-3. to view the full**13 pages of the document.**Department of Management, UTSC

MGEB12 Quantitative Methods in Economics II - Lecture 01

Chapter 9 - Introduction to Hypothesis Testing & Testing of Mean

1. Introduction

•Hypothesis testing – use to determine if statement made about value of population parameter (mean µ,

proportion p, standard deviation σ) should or should not be rejected.

Example – Ambulance company

An ambulance company says they can respond to emergencies with mean time of 12min or less. You take 40

observations and the mean time was 13.25 min. Can you conclude that the “true” mean responds time is less

than 12min? How about if mean time from observations was 12.5min?

•If the true mean is ≤ 12 min what is the chance of you getting mean = 12.5min? Getting mean = 13.25?

Ho = null hypothesis, tentative assumption about population parameter

Ha = alternate hypothesis, opposite of Ho

Procedure

1. State hypothesis you want to test and the desired test significance level

2. Take observations

3. Calculate the test statistic based on the observed data

4. Determine if reject Ho or cannot reject Ho

Conventions

•Manufacture claims usually given benefit of doubt and stated as null hypothesis

•Research question should be expressed as Ha

•The ≤ , ≥ , = should be used in Ho

•The <, >,≠ should be used in Ha

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Example 1

Car currently can do 24 miles/gallon of gas on average. Wondering if new fuel system allows it to go further.

State hypothesis to be tested.

Example 2

Manufacture of soft drink says each bottle filled with at least 67.6 ounces. You want to know if this is true.

State hypothesis to be tested.

Type I and type II errors

•Because hypothesis test base on sample data (eg. 40 observations) and not entire population, errors can

be made

•Define test significance level = α = P[making type I error] = P[incorrectly rejecting Ho given Ho true ]

Typical value of for α used in practice is .1, 0.05 or 0.01

There are 2 approaches to testing:

1. Critical value approach

2. P-value approach

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2. Normal Distribution Review

•Many of the hypothesis test procedures assumes that population is normally distributed.

•Following tends to be normally distributed

oHeight of people

oWeight of people

oScientific measurements

oTest scores

Normal probability density function:

2

2

2

)(

2

1

)(

σ

µ

πσ

−

−

=

x

exf

for -∞ ≤ x ≤ ∞

µ = mean of x

σ = standard deviation of x

•The distribution of X is bell shape.

How to calculate p(x ≤ 2) = ?

dxedxxfxp

x

∫∫

∞−

−

−

∞−

==≤

2

2

)(

2

2

2

2

1

)()2(

σ

µ

πσ

……don’t do this!

•Convert random variable x into standard normal random variable Z and then look up value in Normal

Distribution Table at back of book.

•Given normal random variable x, find standard Normal Random Variable Z:

σ

µ

−

=

x

Z

•Z has mean = 0 and standard deviation = 1

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