5.1             (a)  What is meant by testing a hypothesis?  What is the general procedure?  (b)  What is   meant by type I and type II errors? (c) What is meant by the level  of  significance?  The  level of confidence?

(a)       Testing a hypothesis refers to the acceptance or rejection of an assumption made about an unknown characteristic of a population, such as a parameter or the shape or form of the population distribution. The first step in testing a hypothesis is to make an assumption about an unknown population characteristic. A random sample is then taken from the population, and on the basis of the corresponding sample characteristic, we accept or reject the hypothesis with a particular degree of confidence.

(b)      Type I error refers to the rejection of a true hypothesis. Type II error refers to the acceptance of a false hypothesis. In statistical analysis, we can control or determine the probability of type I or type II errors. The probability of type I error is usually given by the Greek letter alpha (a), while the probability of type II error is represented by a beta ({3). By specifying a smaller type I error, we increase the probability of a type II error. The only way to reduce both a and {3 is to increase the sample size.

(c)       The level of significance refers to the probability of rejecting a true hypothesis or committing type I error (a). The level of confidence (given by 1 - a) refers to the probability of accepting a true hypothesis. In statistical work, the level of significance, a, is usually set at 5%, so that the level of confidence, 1 - a, is 95%. Sometimes a ¼ 1% (so that 1 - a ¼ 99%).