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STA291

STA291. Statistical Methods Lecture 21. 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  …

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STA291

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  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  …

  3. Where do we start? We start with the null hypothesis, H0 About the average miles per gallon of our company’s fleet of cars H0: m = 26 About the average number of chocolate chips in an 18-oz. bag of Chips Ahoy cookies H0: m = 1000 About the average accounting cost incurred when a tax return is audited by the Internal Revenue Service H0: m = $650

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

  5. How do we decide? What about it? Calculate its p-value or … T.S. T.S. How small is small? Is a significance level, or a, given? Find the test statistic About m, so use  or …

  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 • Hypothesis testing for a mean • Assumptions • Appropriate distribution • Test statistic • Parallel of CI with significance testing in two-sided case • Interpretation

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