LESSON 20: PRINCIPLE OF HYPOTHESIS TESTING

So far we have talked about estimating a confidence interval along with the probability (the confidence level) that the true population statistic lies within this interval under repeated sampling. We now examine the principles of statistical inference to hypotheses testing. By the end of this chapter you should be able to • Understand what is hypothesis testing • Examine issues relating to the determination of level of

How is this Done? If the difference between our hypothesized value and the sample value is small, then it is more likely that our hypothesized value of the mean is correct. The larger the difference the smaller the probability that the hypothesized value is correct. In practice however very rarely is the difference between the sample mean and the hypothesized population value larger enough or small enough for us to be able to accept or reject the hypothesis prima-facie. We cannot accept or reject a hypothesis about a parameter simply on intuition; instead we need to use objective criteria based on sampling theory to accept or reject the hypothesis. Hypotheses testing is the process of making inferences about a population based on a sample. The key question therefore in hypotheses testing is: how likely is it that a population such as one we have hypothesized to produce a sample such as the one we are looking at.

significance

• Apply tests of hypotheses to large to management

Situations

• Use of SPSS package to carry out hypotheses test and

interpretation of computer output including p- values

What is Hypothesis Testing?

What is a Hypothesis? A hypothesis is the assumption that we make about the population parameter. This can be any assumption about a population parameter not necessarily based on statistical data. For example it can also be based on the gut feel of a manager. Managerial hypotheses are based on intuition; the market place decides whether the manager’s intuitions were in fact correct. In fact managers propose and test hypotheses all the time. For example: • If a manager says ‘if we drop the price of this car model by

Hypotheses Testing-The theory

Null Hypothesis In testing our hypotheses we must state the assumed or hypothesized value of the population parameter before we begin sampling. The assumption we wish to test is called the Null Hypotheses and is symbolized by Ho. For example if we want to test the hypotheses that the population mean is 500. We would write it as: Ho: µ=500 If we use the hypothesized value of a population mean in a problem we represent it symbolically as: µHo. The term null hypotheses has its origins in pharmaceutical testing where the null hypotheses is that the drug has no effect, i.e., there is no difference between a sample treated with the drug and untreated samples. Alternative Hypothesis If our sample results fail to support the hypotheses we must conclude that something else must be true. Whenever we reject the null hypothesis the alternative hypothesis is the one we have to accept. This symbolized by Ha . There are three possible alternative hypotheses for any Ho., i.e.: Ha: µ≠500(the alternative hypothesis is not equal to 500) Ha: µ>500(the alternative hypothesis is greater than 500) Ha: µ