Inferential Statistics

# Statistical hypothesis test

We call **statistical hypothesis tests** to the procedures that allow you to decide if a hypothesis is accepted or rejected, or determine if observed samples differ significantly from the expected results.

The process to be followed in the statistical hypothesis test has these four steps:

–Step 1: Formulate the null and alternative hypotheses. Both hypotheses are mutually exclusive. The null hypothesis, H_{0}, is the one you have to contrast and it is usually formulated with the idea of being rejected. Depending on the formulating of the alternative hypothesis, H_{1}, the proof of the hypothesis will be bilateral or unilateral.

–Step 2: Determine the rejection and non-rejection (acceptance) region for a determined significance level α. That level is the probability of rejecting the null hypothesis if it is true. α let us limit the rejecting and non-rejecting regions.

–Step 3: Choose the suitable statistic. The statistics that we are going to use are the sample mean, the sample proportion and the difference between sample means. All of them follow a normal distribution. Once we have determined the sample distribution, we define the rejecting region for the null hypothesis.

–Step 4: Make a decision and interpret it. According to the results, we will accept the null hypothesis, with a significance level of α, if this statistic is within the non-rejection region and, otherwise, it will be rejected.

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