STA291Statistical Methods

Lecture 20

We want to make a decision …

About the proportion of successful sales in a region of the country where a new rep works …

Or the proportion of voters who are going to cast a vote for our candidate in an upcoming election …

Or the proportion of new-car buyers who decide to purchase a particular make & model automobile after a major remodel …

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Where do we start?We start with the null hypothesis, H0

About the proportion of successful sales in a region of the country where a new rep works

H0: p = 0.42

About the proportion of voters who are going to cast a vote for our candidate in an upcoming election

H0: p = 0.50

About the proportion of some segment of car buyers who decide to purchase a particular make & model automobile after a major remodel

H0: p = 0.123

Contrasted with?

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The statement of a difference, an increase or decrease, a change; the alternative hypothesis, HA

About the proportion of successful sales in a region of the country where a new rep works

HA: p < 0.42

About the proportion of voters who are going to cast a vote for our candidate in an upcoming election

HA: p > 0.50

About the proportion of some segment of car buyers who decide to purchase a particular make & model automobile after a major remodel

HA: p ≠ 0.12

How do we decide? (and let’s get on with this …)Find the test statisticAbout p, so use

or …

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n

pST

58.042.0

42.0ˆ..

What about it?

T.S.T.S.

Calculate its p-value

or …

How small is small?Is a significance level, or a, given?

ExampleOn the old website, 20% of visits to

SmartWool’s page resulted in a sale. Suppose you collect a sample of 200 visits to the new page and find that 58 have resulted in a sale.

A) Frame appropriate null and alternative hypotheses for the proportion of sales that result in a sale.

B) Based on this sample and = 0.05, does the new website generate more sales per visit?

Looking back

oHypothesis testing for a proportionoAssumptionsoTest statisticoTwo-tailed testoInterpretation