7 Comparing Population Means

Where We’ve Been

  • Explored two methods for making statistical inferences: confidence intervals and tests of hypotheses

  • Studied confidence intervals and tests for a single population mean μ, a single population proportion p, and a single population variance σ2

  • Learned how to select the sample size necessary to estimate a population parameter with a specified margin of error

Where We’re Going

  • Learn how to identify the target parameter for comparing two population means (7.1)

  • Learn how to compare two means by using confidence intervals and tests of hypotheses (7.27.3)

  • Determine the sizes of the samples necessary to estimate the difference between two population means with a specified margin of error (7.4)

  • Present nonparametric tests for comparing two populations (7.57.6)

  • Learn how to compare three or more population means using a designed experiment (7.7)

Statistics in Action ZixIt Corp. v. Visa USA Inc.—A Libel Case

The National Law Journal (Aug. 26–Sept. 2, 2002) reported on an interesting court case in volving ZixIt Corp., a start-up Internet credit card clearing center. ZixIt claimed that its new online credit card processing system would allow Internet shoppers to make purchases without revealing their credit card numbers. This claim violated the established protocols of most major credit card companies, including Visa. Without the company’s knowledge, a Visa vice president for technology research and development began writing e-mails and Web site postings on a Yahoo! message board for ZixIt investors, challenging ZixIt’s claim and urging investors to sell their ZixIt stock. The Visa executive posted over 400 e-mail and notes before he was caught. Once it was discovered that a Visa executive was responsible for the postings, ZixIt filed a lawsuit against Visa Corp., alleging that Visa—using the executive as its agent—had engaged in a “malicious two-part scheme to disparage and interfere with ZixIt” and its efforts to market the new online credit card processing system. In the libel case ZixIt asked for $699 million in damages.

Dallas lawyers Jeff Tillotson and Mike Lynn, of the law firm Lynn Tillotson & Pinker, were hired to defend Visa in the lawsuit. The lawyers, in turn, hired Dr. James McClave (co-author of this text) as their expert statistician. McClave testified in court on an “event study” he did matching the Visa executive’s e-mail postings with movement of ZixIt’s stock price the next business day. McClave’s testimony, showing that there was an equal number of days when the stock went up as went down after a posting, helped the lawyers representing Visa to prevail in the case. The National Law Journal reported that, after two and a half days of deliberation, “the jurors found [the Visa executive] was not acting in the scope of his employment and that Visa had not defamed ZixIt or interfered with its business.”

In this chapter, we demonstrate several of the statistical analyses McClave used to infer that the Visa executive’s postings had no effect on ZixIt’s stock price. The daily ZixIt stock prices as well as the timing of the Visa executive’s postings are saved in the ZIXITVISA file.* We apply the statistical methodology presented in this chapter to this data set in two Statistics in Action Revisited examples.

Statistics in Action Revisited

  • Comparing Mean Price Changes (p. 379)

  • Comparing Price Changes using a Nonparametric Test (p. 408)

Data Set: ZIXITVISA

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