One or Two Tailed Hypothesis Tests? Discussion

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Hypothesis tests take one of two forms:

One Tailed Tests – A claim is involved, or there is suspicion that the frequency, mean or proportion has increased or decreased. For example, a manufacturer of cat food claim 8 out of ten cats prefer his company’s cat food to any other company, or a new safety procedure gas been introduced. The accident rate has decreased slightly and it must be evaluated whether this is decrease is statistically significant. Suppose we are test whether the mean of a population has increased. We would conduct the test based on the hypotheses:

Two Tailed Tests – The more objective test. It needs to be decided whether a proportion, mean or frequency has changed. In fact it will usually be the fact that the frequency, mean, proportion, standard deviation or other quantity is not the same for a sample from that stated in the null hypothesisThe purpose of the hypothesis test is to find whether or not the difference is statistically significant. Because the quantity is always either bigger or smaller than the quantity as given in the null hypothesis, the obvious question arises: why do we need two tailed 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 or smaller than the valuegiven in the null hypothesis, and if it is bigger, conduct the test given above? We don’t do this for two reasons:

  1. We are only testing whether the mean has changed. If we conduct only one tailed tests, we won’t be rejecting the null hypothesis enough.
  2. There is another type of hypothesis test based on finding the “critical values” of the observations, using the null distribution, which would result in the null hypothesis being reject. Hypothesis tests based on on probabilities or test statistics must be conducted once for each test, but hypothesis tests based on critical values can be carried out many times with little extra effort. This sort of test is especially useful if we want to find out if a test statistic is changing over time – for example if a machine alignment is moving out of true. The critical values can be written on the side of a machine and used by a production worker who knows nothing about statistics. If only one tailed tests were use here, only one type of misalignment would be caught, for example, only those for whichand not those for which
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