when a hypothesis test is set up to show that the sample mean would be only higher than the population mean this is referred to as a one tailed test a formulation of this hypothesis would be for example that the returns on an investment fund would be at least x one tailed tests could also be set up to show that the sample mean could be only less than the population mean the key difference from a two tailed test is that in a two tailed test the sample mean could be different from the population mean by being either higher or lower than it 
if the sample being tested falls into the one sided critical area the alternative hypothesis will be accepted instead of the null hypothesis a one tailed test is also known as a directional hypothesis or directional test a two tailed test on the other hand is designed to examine both sides of a specified data range to test whether a sample is greater than or less than the range of values example of a two tailed testas a hypothetical example imagine that a new stockbroker named xyz claims that their brokerage fees are lower than that of your current stockbroker abc data available from an independent research firm indicates that the mean and standard deviation of all abc broker clients are 18 and 6 respectively a sample of 100 clients of abc is taken and brokerage charges are calculated with the new rates of xyz broker if the mean of the sample is 18 75 and the sample standard deviation is 6 can any inference be made about the difference in the average brokerage bill between abc and xyz broker this calculated z value falls between the two limits defined by z2 5 1 96 and z2 5 1 96 this concludes that there is insufficient evidence to infer that there is any difference between the rates of your existing broker and the new broker therefore the null hypothesis cannot be rejected alternatively the p value p z 1 25 p z 1 25 2 0 1056 0 2112 21 12 which is greater than 0 05 or 5 leads to the same conclusion 