Formulating Null and Alternative Hypotheses

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Every hypothesis test seeks to prove or disprove a statistical statement about a population to a particular level of certainty. In order to do this the statement needs to be clearly phrased.

Typically the statement is about the mean of a distribution or the probability of an event occurring. The null hypothesis is the value that we suppose this mean or probability has for a certain probability distribution. This can be because, for example:

  1. The mean(or probability) has had this value,(or) for a while, and we want to see if the latest set of data indicates a change. In this case, our null hypothesiswould be that the mean(or probability) has this longstanding value and the alternative hypothesis is(or).

  2. That some manufacturer has made a claim about the superiority of his product over the product of some other manufacturer. He might claim that 80% of cats prefer the ‘Catlove’ brand of catfood, manufactured by his company. In this casecould beand the alternative hypothesis could be

When the null and alternative hypotheses are drawn up, there is often a claim that is to be tested. In the first claim above, there is no claim of increase of the mean, so the hypothesis test is conducted merely in order to see if there is evidence that the mean (or probability) has changed, not specifically increased or decreased. Of course, in order to change, the mean (or probability) must either increase or decrease, but the assumption is not part of the test. In the second example above, the manufacturer of cat food is making a suspect claim about the love of cats for his company’s brand of cat food, and it must be suspected that in fact less than 80% of cats prefer his company’s brand. In this case therefore, as stated above, the null hypothesis would be that

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