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Department of Management, UTSC

ECMB12 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

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

[pic]

• Define test significance level = α = P[making type I error] =...

ECMB12 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

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

[pic]

• Define test significance level = α = P[making type I error] =...

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