Question

Which of the elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test

Short answer

The elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test are null hypothesis, alternative hypothesis, test statistic, and rejection region.

Step-by-step solution

Given information

The information regarding the test hypothesis.

The test hypothesis can be used to conduct the test.

State the statistical hypothesis test

Hypothesis testing is a method in which statistical data from a group sample is drawn to reach a conclusion about population parameters. Generally, it is used when you want to compare two or more groups.

Explain the elements of a test hypothesis used to conduct the test prior to analyzing the data

Before performing any test of hypothesis, we must specify the null and alternative hypothesis as well as the desired level of significance $\alpha$.

The given four elements are specified before the sampling experiment is performed.

Null Hypothesis $\left(H_0\right)$:

The null hypothesis is the theory about the specific values of one or more population parameters. The theory is always stated as $H_0$: parameter=value.

Alternative Hypothesis $\left(H_a\right)$:

The alternative hypothesis is a theory that contradicts the null hypothesis. The theory represents that which we will adopt only when sufficient evidence exists to establish its truth.

Test statistic:

A sample statistic is used to decide whether to reject the null hypothesis.

Rejection region:

The numerical values of the test statistic for which the null hypothesis will be rejected.

Hence, the elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test are null hypothesis, alternative hypothesis, test statistic, and rejection region.