Performing a basic hypothesis test for your project

Let us consider an example, manager of a pipe manufacturing facility must ensure that the diameters of its pipes equal 5cm. The manager follows the basic steps for doing a hypothesis test.

You can follow this basic step to correctly set up and perform a hypothesis test

You should determine the criteria for the test and the required sample size before you collect the data.

  1. Specify the hypotheses.

First, the manager formulates the hypotheses. The null hypothesis is: The population mean of all the pipes is equal to 5 cm. Formally, this is written as: H0: μ = 5

Then, the manager chooses from the following alternative hypotheses:

Condition to testAlternative Hypothesis
The population mean is less than the sided: μ < 5
The population mean is greater than the sided: μ > 5
The population mean differs from the target.two sided: μ ≠ 5
Conditions and corresponding alternative hypothesis

Because they need to ensure that the pipes are not larger or smaller than 5 cm, the manager chooses the two-sided alternative hypothesis, which states that the population mean of all the pipes is not equal to 5 cm. Formally, this is written as H1: μ ≠ 5

  1. Choose a significance level (also called alpha or α).

The manager selects a significance level 0.05, which is the most commonly used significance level.

  1. Collect the data.

They collect a sample of pipes and measure their diameters.

  1. Compare the p-value from the test to the significance level.

After they perform the hypothesis test, the manager obtains a p-value of 0.004. The p-value is less than the significance level of 0.05.

  1. Decide whether to reject or fail to reject the null hypothesis.

The manager rejects the null hypothesis and concludes that the mean pipe diameter of all pipes is not equal to 5cm.