STAT 301 - Business Statistics
Lecture Review #14 - More on Hypothesis Testing

Review questions:

1) What is meant in statistics by the term significant? How does this differ from ordinary, nontechnical usage of the word?

2) What is a one-tailed test? What determines whether a one- or two-tailed test should be used?

Computational exercises:

Do all six steps of the following hypothesis testing problems:

1) During the 2023 National Football League regular season, the home team won 151 games and lost 121 games. Perform an appropriate hypothesis test to answer the research question: Does the home team enjoy a home-field advantage in professional football?

2) In a "bold gamble to revive depressed sales," the Joseph Schlitz Brewing Co. announced that it would broadcast on live television a taste test featuring 100 beer drinkers during half time of a National Football League AFC wildcard playoff game. During the live broadcast, Schlitz claimed that the 100 beer drinkers selected for the taste test were "loyal" drinkers of Budweiser, the industry's best-selling beer. Each of the participants was served two beers, one Schlitz and one Budweiser, in unlabelled ceramic mugs. Tasters were then told to make a choice by pulling an electronic switch left or right in the direction of the beer they preferred. (Prior to the test, the tasters were informed that one of the mugs contained their regular beer, Budweiser, and the other contained Schlitz, but the ordering was not revealed.) The percentage of the 100 "loyal" Budweiser drinkers who preferred Schlitz was then tabulated live, in front of millions of football fans. An Orlando Sentinel story on the event reported

One beer industry observer was quoted as calling the test "a giant roll of the dice" in Schlitz' effort to gain a bigger share of the $8.5 billion beer industry. ... Schlitz, a one-time brewery giant, has seen its sales tumble from 16 million barrels ... to between 7 and 9 million barrels. ... However, Frank Sellinger, the newly appointed Chief Executive at Schlitz, disagrees that the move was a gamble: "Some people thought it was risky to do live TV taste tests. But it didn't take nerve, it just took confidence."

The results of the live TV taste test showed that 46 of the 100 "loyal" Budweiser drinkers preferred Schlitz. Schlitz, of course, labeled the outcome "an impressive showing" in a magazine advertisement following the test. Dr. Rasp is a bit more cynical about the whole process. He claims that most people can't tell one beer from another (or from another liquid of similar color, for that matter). Are the data consistent with Dr. Rasp's explanation?

SOLUTIONS:
1) z=1.819, p-value=0.034 [one-tailed]. Reject H₀, concluding home team has advantage.
2) z=0.80, p-value=0.212 [one-tailed]. Don't reject H₀.