Hypothesis test

A procedure that evaluates two mutually exclusive statements about a population. A hypothesis test uses sample data to determine which statement is best supported by the data. These two statements are called the null hypothesis and the alternative hypotheses. They are always statements about populations 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. Examples of questions you can answer with a hypothesis test include:

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

· Is the standard deviation of their height equal to 5 inches?

· Are male and female undergraduates equal in height?

· Does the height of female undergraduates follow a normal distribution?

To illustrate the process, the manager of a pipe manufacturing facility must ensure that the inside diameters of its pipes equal 5cm. She takes a sample of pipes, measures their inside diameters, and conducts a hypothesis test on the mean inside pipe diameter. First, she must formulate her hypotheses.

Null Hypothesis: H0

States that a population parameter is equal to a desired value. The null hypothesis for the pipe example is:

H0: m = 5

Alternative Hypothesis: H1 or HA

States that the population parameter is different than the value of the population parameter in the null hypothesis. In the example, the manager chooses from the following alternative hypotheses:

If the manager thinks...	She will formulate H1 to be...
the true population mean is less than the target...	one-sided: m < 5
the true population mean is greater than the target...	one-sided: m > 5
the true population mean differs from the target, but she does not know in which direction it differs...	two-sided: m ≠ 5

After formulating her null and alternative hypotheses, the manager performs her hypothesis test. The test calculates the probability of obtaining the observed sample data under the assumption that the null hypothesis is true. If this probability (the p-value) is below a user-defined cut-off point (the a-level), then this assumption is probably wrong. Therefore, she would reject the null hypothesis and conclude in favor of the alternative hypothesis. So, if the manager performs a hypothesis test with a two-sided H1 and obtains a p-value of 0.005, she rejects the null hypothesis and concludes that the mean inside pipe diameter of all pipes is not equal to 5cm.