AS/A2 Stats 1 Stats 3

S2 Topic 4: Hypothesis tests
One and two tailed tests
In a hypothesis test: the null hypothesis H0 is a statement which is to be "accepted" unless evidence proves otherwise. Acceptance does not mean that we have proved the statement to be true, but only that there is insufficient evidence to disprove it. A null hypothesis might involve the population mean, for example m = 100. the alternative hypothesis H1 can take a number of forms. If it is thought that the alternative to the null hypothesis being true is simply that it is not true, then a typical alternative hypothesis could be m ¹ 100. This would be called a two-tailed test. It maybe be strongly suspected that the true mean may be greater than some given value, for example m > 100. This is a one-tailed test.	One-tailed test: H0 m=m0 H1 m<m0 One-tailed test: H0 m=m0 H1 m>m0 Two-tailed test: H0 m=m0 H1 m ¹m0
In the diagram above, m0 refers to an assumed value for the mean of the distribution being studied; m refers to the "true mean".

Summary In any hypothesis test we are testing the evidence to see if it is sufficient to reject the null hypothesis. © MathsNet 2001