"The Lady Tasting Tea" : Can tea poured into milk taste differently than that of milk poured into tea? This experiment was originally designed by Professor Ronald Fisher and it will help us motivate the discussion of hypothesis testing. We will, however, use Coke and Pepsi in our experiment.
Type I error : In 1959, Steven Truscott was found guilty of murdering his classmate even though he did not commit any crime. In 2007, he was formally acquitted of the crime. In 2008, the government of Ontario awarded him $6.50 million in compensation
Type II error : Many people believe that O. J. Simpson had murdered his wife and he should have been found guilty. But after a lenghty trial, he was acquitted in 1995.
Cigarette smoking machines can measure the tar and nicotine content of cigarettes. If the manufacturer and a health group make different claims, we can test them using hypothesis testing. [Trivia for history buffs: Who was the most famous Gaul whose helmet appears on the cigarette pack in the above link? (Even Asterix wears the same helmet.) Hint: The French people are very proud of him since he bravely fought Julius Caesar in 52 BC, but was eventually defeated and executed. See here.]
DeGroote GMAT scores (2005) : In 2005, the mean GMAT scores of our entering students was approximately 630 with a standard deviation of approximately 45. Before the admissions are finalized, we have data for 25 newly admitted students with a sample average score of 625. Do we have a good reason to believe that the true mean (when admissions close) will be at least as much as in 2005? Shall we reject the null hypothesis H0: μ ≥ 630?
Tar content of Gauloises cigarettes. Here we have a sample of 10 observations and so use the t-test. We don't have sufficient evidence to reject H0 since p = 0.3049.
MER of mutual funds : This link relates to Problem 8.84 on page 270. Different mutual funds companies charge different MERs (management expense ratio) which could be as high as 3% (or even more), see, for example, Sceptre's MERs for Global Equity Funds. Some banks charge a much lower MER if you invest in stock indices (index funds), see, for example, the MERs for TD Canada Trust eFunds.
This problem is to use hypothesis testing and see if the current average MERs exceed what we had 10 years ago.
