1. STA291 Statistical Methods Lecture 21

2. We want to make a decision … About whether our company’s fleet of cars has failed to meet our goal average of 26 miles per gallon… Or whether Chips Ahoy ® cookies really have as many chocolate chips in them as claimed … Or the average accounting cost incurred when having your tax return audited by the Internal Revenue Service  … 2

3. Where do we start? We start with the null hypothesis, H 0 About the average miles per gallon of our company’s fleet of cars H 0 :  = 26 About the average number of chocolate chips in an 18-oz. bag of Chips Ahoy cookies H 0 :  = 1000 About the average accounting cost incurred when a tax return is audited by the Internal Revenue Service H 0 :  = $650 3

4. Contrasted with? 4 The alternative hypothesis, H A About the average miles per gallon of our company’s fleet of cars H A :  < 26 About the average number of chocolate chips in an 18- oz. bag of Chips Ahoy cookies H A :  > 1000 About the average accounting cost incurred when a tax return is audited by the Internal Revenue Service H A :  ≠ $650

5. How do we decide? Find the test statistic About , 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, SmartWool’s average sale was $24.85. Of the 58 sales made on SmartWool’s new website, the average sale was $26.05 with a standard deviation of 10.2. A) Frame appropriate null and alternative hypotheses for the average from SmartWool’s website. B) Based on this sample and = 0.05, does the new website generate a higher average sale?

7. Looking back o Hypothesis testing for a mean o Assumptions o Appropriate distribution o Test statistic o Parallel of CI with significance testing in two-sided case o Interpretation