1 / 7

Hypothesis Testing in Statistical Methods: Evaluating Mileage, Cookies, and Tax Costs

This lecture explores hypothesis testing for three separate cases: evaluating whether a car fleet meets a mileage goal, assessing if Chips Ahoy cookies contain the claimed amount of chocolate chips, and calculating the average cost of tax return audits. It introduces the null hypothesis (H0) for each scenario and contrasts it with the alternative hypothesis (HA). The lecture discusses calculating p-values, determining significance levels, and framing appropriate hypotheses, using real-world examples from sales data on SmartWool's old and new websites.

mayes
Télécharger la présentation

Hypothesis Testing in Statistical Methods: Evaluating Mileage, Cookies, and Tax Costs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related