H0 : | π > 0.5 |
HA : | π < 0.5 |
Sample of voting intentions, π = P(Mike Smith)
Use the diagrams on this page to discuss the difference between the null and alternative hypothesis and to explain how the data are used to weigh the evidence against H0.
The page initially shows an example where the two competing hypotheses have equal status — either Mike Smith or Sarah Brown winning the election. Drag the slider to see how we would interpret different numbers in our sample supporting the two candidates. Note that:
Select Null and alternative hypotheses from the pop-up menu. The difference is that:
We never try to 'prove' that H0 holds, though we may be able to 'prove' that HA holds.
Drag the slider to see the conclusions we would reach from different sample means. Note that:
When the sample mean is near 0.0, we conclude that the data are consistent with H0, but we should never conclude that H0 is true
Even if it is exactly 0.0, µ could just as easily be 0.0001 or -0.0002.
Voting intentions
Two candidates, Mike Smith and Sarah Brown, stand for election as chairperson of the board of directors of a large company. Just before the shareholders' meeting at which the election will be held, 56 randomly selected shareholders are asked about their voting intentions.
Market share estimation through audits
The traditional retail store audit is a widely used marketing research tool among consumer packaged goods companies. The retail stort audit involves periodic audits of a sample of retail audits to monitor inventory and purchases of a particular product. Another auditing procedure, weekend selldown audits, has been proposed as a less expensive alternative.
The market shares of 10 brands of fruit juice were estimated using both of the store audit methods. Do the two methods result in the same estimates, on average? The data are paired, so we analyse the difference in estimates for each product (traditional minus weekend selldown) and test whether the underlying population mean of these values is zero.