One or Two Tailed Hypothesis Tests - Discussion

Hypothesis tests take one of two forms:

One Tailed Tests – A claim is involved, or there is suspicionthat the frequency, mean or proportion has increased or decreased.For example, a manufacturer of cat food claim 8 out of ten catsprefer his company's cat food to any other company, or a new safetyprocedure gas been introduced. The accident rate has decreased slightly and it must be evaluated whether this is decrease isstatistically significant. Suppose we are test whether the mean of apopulation has increased. We would conduct the test based on thehypotheses:

Two Tailed Tests – The more objective test. It needs to bedecided whether a proportion, mean or frequency has changed. In factit will usually be the fact that the frequency, mean, proportion,standard deviation or other quantity is not the same for a samplefrom that stated in the null hypothesisThepurpose of the hypothesis test is to find whether or not thedifference is statistically significant. Because the quantity isalways either bigger or smaller than the quantity as given in thenull hypothesis, the obvious question arises: why do we need twotailed tests at all? If we are testing whether the mean has changed,why can't we find the mean of a sample, see whether it is larger orsmaller than the valuegivenin the null hypothesis, and if it is bigger, conduct the test givenabove? We don't do this for two reasons:

  1. We are only testing whether the mean has changed. If weconduct only one tailed tests, we won't be rejecting the nullhypothesis enough.

  2. There is another type of hypothesis test based on finding the“critical values” of the observations, using the nulldistribution, which would result in the null hypothesis beingreject. Hypothesis tests based on on probabilities or teststatistics must be conducted once for each test, but hypothesistests based on critical values can be carried out many times withlittle extra effort. This sort of test is especially useful if wewant to find out if a test statistic is changing over time - forexample if a machine alignment is moving out of true. The criticalvalues can be written on the side of a machine and used by aproduction worker who knows nothing about statistics. If only onetailed tests were use here, only one type of misalignment would becaught, for example, only those for whichandnot those for which