A hypothesis test is a statistical test that is used to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. Hypothesis testing involves defining two mutually exclusive statements, and then using sample data to determine which statement is best supported by the facts. These two statements are called the null hypothesis and the alternative hypotheses. They are always statements about population attributes, such as the value of a parameter, the difference between corresponding parameters of multiple populations, or the type of distribution that best describes the population.

Hypothesis testing gives answers to practical questions such as:

· Is the mean height of undergraduate women equal to 66 inches?

· Is the mean height of undergraduate men greater than undergraduate women?

· Is performance on shift A different from shift B?

· Does my new process perform better than my old process?

Hypothesis testing provides objective, data driven answers to questions which are traditionally answered subjectively. For example, we make a change to a process and look at the data before and after. It appears that the mean performance has improved so we conclude that our change has been successful, but how confident are we that this is really the case? What is the risk if we conclude that there has been a change when in fact actually there has not been a change? Assume that we only have a few days of data and we will either invest or not invest a large sum of money based on the answer!

Setting up and testing hypotheses is an essential part of statistical inference and it quantifies the risk associated with the decision making process.

Hypothesis Testing has four stages:

1. Practical Question - State the question you want answered in practical terms.

2. Statistical Question – Turn this into a statistical question, by formulating two hypotheses, the null (Ho) and the alternative (Ha). The null hypothesis assumes that there is no change, ...