1. STA291 Statistical Methods Lecture 20

2. 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 … 2

3. Where do we start? We start with the null hypothesis, H 0 About the proportion of successful sales in a region of the country where a new rep works H 0 : p = 0.42 About the proportion of voters who are going to cast a vote for our candidate in an upcoming election H 0 : 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 H 0 : p = 0.12 3

4. Contrasted with? 4 The statement of a difference, an increase or decrease, a change; the alternative hypothesis, H A About the proportion of successful sales in a region of the country where a new rep works H A : p < 0.42 About the proportion of voters who are going to cast a vote for our candidate in an upcoming election H A : 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 H A : p ≠ 0.12

5. How do we decide? (and let’s get on with this …) Find the test statistic About p, so use  or … 5 What about it? T.S. Calculate its p-value or … How small is small? Is a significance level, or , given?

6. Example On 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?

7. Looking back o Hypothesis testing for a proportion o Assumptions o Test statistic o Two-tailed test o Interpretation