1 / 7

Hypothesis Testing: Evaluating Fleet MPG, Cookie Chips, and Tax Audit Costs

In this lecture, we dive into hypothesis testing to evaluate various claims. We consider whether our company's fleet of cars meets the average goal of 26 miles per gallon, examine the true chocolate chip content in Chips Ahoy! cookies, and analyze the average accounting costs associated with tax audits by the IRS. We introduce null (H0) and alternative hypotheses (HA) for each case and discuss how to calculate p-values and test statistics. Through examples, we learn to interpret results and understand their significance in decision-making.

shamus
Télécharger la présentation

Hypothesis Testing: Evaluating Fleet MPG, Cookie Chips, and Tax Audit 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