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 president of a student council. Four days before the election, the student newspaper asks 56 randomly selected students about their voting intentions.
Memory test before & after exercise
Forty students in a psychology class are given a memory test. After a 30-minute session where the students undertake a variety of physical exercises, the students are given another similar memory test. Has exercise has affected memory? We analyse the difference in test results for each student ('after exercise' minus 'before exercise') and test whether the underlying population mean of these values is zero.