The Null and Alternative Hypotheses

In his role as the decision maker, a business manager encounters many situations that require him to estimate certain population parameters. Statistical inference is the estimation of a population parameter based on a sample of the population. One very important aspect of statistical inference is hypothesis testing. Hypothesis testing requires you, the manager of Company W, to start your research with a certain belief regarding the value of your population parameter. This is the value that is expected to be the correct, acceptable or required value of that parameter. You then use sample data to either accept or refute the initial belief (Casella & Berger, 2002).

For example, the plant manager at a Coca-cola plant may note that his plant produces about 500,000 pieces of 12 oz Coca-cola cans. With such a high number, it would be impossible to determine the exact amount of fluid that is injected into each can. Instead, the plant manager only targets to ensure that the mean of all the soda filled into the bottles will be about 12 oz. Like every other production process, some of the cans will contain slightly lower amounts while others will contain slightly higher amounts. The important thing for the manager is to ensure that the mean amount of soda is kept around 12 oz. To control this, the plant manager picks a random sample from the population and calculates its mean once every two hours. His belief is that the filling machine is filling the cans with an average of 12 oz. This is the manager’s hypothesis. He rejects the hypothesis if he finds a substantial difference in the amount of fluid put in the cans. In a case where the hypothesis is refuted, some action would require to be taken to improve the delivery of the machine.

In hypothesis testing, a null hypothesis and an alternative hypothesis are formulated. The null hypothesis contains an equal sign and is denoted as H₀. The alternative hypothesis, on the other hand, is the opposite of the null hypothesis. Based on a study, the null hypothesis is either rejected or not rejected. Correctly identifying a null hypothesis and an alternative hypothesis is vital and an error could provide misleading data (Casella & Berger, 2002).

Hypothesis testing is often used to determine if a situation has changed. In that case, it is referred to as testing the status quo. In the case of the Coca-Cola Company, the plant manager would assume that the machine is working properly at the beginning of production. He could then check every two hours to ensure that the situation has not changed. In this case, therefore, the null hypothesis and the alternative hypothesis are:

      H₀; µ= 12 oz

      H₁; µ ≠ 12 oz

As long as the mean remains reasonably close to 12 oz, the manager will assume that the machine is working properly. Otherwise, he will reject the null hypothesis and set out to identify and fix the problem (Storey, 2002).

There are three possible formulations of the null hypothesis. The three possibilities are often used in different situations. It is either =, ≤, or ≥. Whichever the case, the alternative is the absolute opposite which is usually, ≠, > or < respectively. You should note that there is no situation where the manager is required to accept the alternative hypothesis. Instead, he is required to reject the null hypothesis if there exists a situation where the alternative hypothesis is found to be significantly true. The null hypothesis is also never expected to be exact. Instead, it is expected to fall within a certain range. This range factors in a certain error that is allowed in the machine. This error is known as a significant error (Storey, 2002).

References

Casella, G., & Berger, R. L. (2002). Statistical inference. Australia: Thomson Learning.

Storey, J. D. (2002). A direct approach to false discovery rates. Journal of The Royal Statistical Society Series B-statistical Methodology. doi:10.1111/1467-9868.00346