What is Hypothesis Testing?

Hypothesis testing is an essential technique in statistics, used often in science to make experimental conclusions. Hypothesis testing is a formal process for evaluating claims about the probability distribution of some population with only some sample from actual population. A common misconception about hypothesis testing is that hypothesis testing can prove the hypothesis. Instead, it only indicates whether the hypothesis is supported by the sample data or not.

Statistics hypotheses

Statistics hypotheses are proposed by observing data and stated in such a way that they can be evaluated by appropriate statistical techniques.

Hypothesis testing can examine two opposing statistics hypothesis: null hypothesis testing ($H_0$) and Alternative hypothesis ($H_1$). The null hypothesis is the statement being tested and usually is a statement of "no effect" or "no difference". The alternative hypothesis is the statement that you want to be able to conclude is true and is usually is opposite of the null hypothesis. In hypothesis testing, we always assume the null hypothesis is true. A test will remain with the null hypothesis until there is enough evidence to support the alternative hypothesis.

Common hypothesis

If we want to determine whether a population mean, $\mu$, is equal to some target value $\mu_0$, null hypothesis and alternative hypotheses can be constructed as following:

• $H_0: \mu = \mu_0$
• $H_1: \mu < \mu_0$ (a lower-tailed test) or
• $H_1: \mu > \mu_0$ (a upper tailed test) or
• $H_1: \mu \neq \mu_0$ (a two-tailed test)

As an example, consider a manufacturer of computer devices. The manufacturer has a process which coats a computer part with a material that is supposed to be 100 microns thick (one micron is $\frac{1}{1000}$ of a millimeter). If the coating is too thin, then proper insulation of the computer device will not occur and it will not function reliably. Similarly, if the coating is too thick, the device will not fit properly with other computer components.

The manufacture want to calibrate the machine that applies the coating so that it has an average coating depth of 100 microns with a standard deviation of 10 microns.

Therefore, our hypotheses can be stated as: $H_0$: The average coating depth is 100 microns. $H_1$: The average coating depth is not equal to 100 microns.

Common questions we can answer with a hypothesis test

Here are some examples of questions we can answer with a hypothesis test include:

• Does the mean height of undergraduate women differ from 66 inches?
• Is the standard deviation of their height equal less than 5 inches?
• Do male and female undergraduates differ in height?