Fundamentals of Hypothesis Designing and Testing - Essay Example

Definition: A statistical hypothesis is an assertion regarding the distribution of a variable or variables. If a statistical hypothesis completely specifies the distribution, it is referred to as a simple hypothesis; if not, it is referred to as a composite hypothesis (Goodman, 1999). The testing of a statistical hypothesis is the application of an explicit set of rules for deciding whether to accept the hypothesis or to reject it (Hinkelmann & Kempthorne, 2008). The method of conducting any statistical hypothesis testing can be outlined in six steps: The alternative hypothesis, which we denote by H1, expresses the idea of some difference.

Alternative hypotheses may be one or two sided (Kaye & Freedman, 2011). Usually, the setting of the problem determines the alternative even before the data has been collected. • Type II error: Reject H1 whilst factual; the chance of making a type II error is symbolized by {3. The objective in all hypothesis testing is to set the Type I error level, also known as the significance level, at a low enough value, and then to use a test statistic which minimizes the Type II error level for a given sample size.

As we fix the Type I error level, it is best to devise the test in a way that the Type I error is most serious, in terms of cost (Lehmann & Romano, 2005). A critical P -value is the probability that is set by the person doing the test; it is the threshold for the P-value that the tester will use to decide whether the sample is unusual enough, compared to the hypothesized population, to indicate that the null hypothesis should be turned down in favor of the other option (McCloskey & Stephen, 2008).

The calculated test statistic is compared to the sampling distribution that the statistic would have if the null hypothesis was factual. The comparison is summarized into a probability called a P-value: this is the probability, if the null hypothesis is factual, that the statistic would be at