Testing hypotheses using t-tests

One of the most common tasks in statistics is to test the validity of a hypothesis about the mean of a normally distributed population, given that you have collected sample data from that population. For example, in quality control, we might wish to test that the thickness of a sheet produced at a mill is 2 mm. To test this, we can randomly select sample sheets and measure the thickness to obtain our sample data. Then, we can use a t-test to test our null hypothesis, , that the mean paper thickness is 2 mm, against the alternative hypothesis, , that the mean paper thickness is not 2 mm. We can use the SciPy stats module to compute a t statistic and a value. If the value is below 0.05, then we accept the null hypothesis with 5% significance (95% confidence). If the value is larger than 0.05, then we must reject the null hypothesis in favor of our alternative hypothesis.

In this recipe, we will learn how to use a t-test to test whether the assumed...