Challenge Level

Give convincing reasons why that is the case. If a statement is false, can you give an example to show why? And if so, is there some sense in which the statement is "usually" true, but there are just a few special cases where it is false, or is it "usually" false?

- A significance level of 5% means that there is a 5% probability of getting a test statistic in the critical region if the null hypothesis is true.
- A significance level of 5% means that there is a 5% probability of the null hypothesis being true if the test statistic lies in the critical region.
- The p-value of an experiment gives the probability of the null hypothesis being true.
- If the p-value is less than 0.05, then the alternative hypothesis is true.
- If the p-value is less than 0.05, then the alternative hypothesis is more likely to be true than the null hypothesis.
- The closer the p-value is to 1, the greater the probability that the null hypothesis is true.
- If we have a larger sample size, we will get a more reliable result from the hypothesis test.
- If we repeat an experiment and we get a p-value less than 0.05 in either experiment, then we must reject the null hypothesis.
- If we do not get a significant result from our experiment, we should go on increasing our sample size until we do.

The XKCD cartoon Significant provides a nice illustration of the idea in question 8.