Chapter 20: Testing Hypotheses About Proportions. Unit 5. AP Statistics. Hypotheses. Hypotheses are working models that we adopt temporarily. Our starting hypothesis is called the null hypothesis .
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H0: parameter = hypothesized value.
A 1996 report from the U.S. Consumer Product Safety Commission claimed that at least 90% of all American homes have at least one smoke detector. A city’s fire department has been running a public safety campaign about smoke detectors consisting of posters, billboards, and ads on radio and TV and in the newspaper. The city wonders if this concerted effort has raised the local level above the 90% national rate. Building inspectors visit 400 randomly selected homes and find that 376 have smoke detectors. Is this strong evidence that the local rate is higher than the national rate? Set up the hypotheses.
using the statistic
Calculate your test statistic
Draw a picture of your desired area under the t-model, and calculate your P-value.
Make your conclusion.
When your P-value is small enough (or below α, if given), reject the null hypothesis.
When your P-value is not small enough, fail to reject the null hypothesis.
Home field advantage –teams tend to win more often when the play at home. Or do they?
If there were no home field advantage, the home teams would win about half of all games played. In the 2007 Major League Baseball season, there were 2431 regular-season games. It turns out that the home team won 1319 of the 2431 games, or 54.26% of the time.
Could this deviation from 50% be explained from natural sampling variability, or is it evidence to suggest that there really is a home field advantage, at least in professional baseball?