Models, p-values, and hypotheses

Abstract This chapter is concerned with testing hypotheses concerning relevant features of the unknown population. Examples are: the hypothesis that the population mean has a certain value; the hypothesis that the probability of a particular event is a specified amount; the hypothesis that events occur at random times, the hypothesis that two samples have been drawn fro the same population. The framework for testing such hypotheses requires the analyst to specify an alternative to the ‘null’ hypothesis of interest. The alternative might be ‘the value is not the one specified’ or it might be one-sided: ‘the value is greater than that’. The key to testing a hypothesis is the so-called pvalue which is the probability of the observed value, or a more extreme value, occurring by chance if the null hypothesis were correct. A p-value of between 1% and 5% should alert the analyst to look closely at the situation, while any smaller p-value would be regarded as a clear sign that the null hypothesis was incorrect.