General Procedure

2. Statistics and their sample distribution

1.Formulation of hypotheses

Hypothesis testing is a statistical tool that aims to make inferences about populations. The first step is to formulate two or more hypotheses to test them. Hypotheses indicate that a random variable has a specific distribution or value. The first hypothesis, called the null hypothesis, is denoted by H0, thus indicating that there is no difference. The second hypothesis, which is called the alternative hypothesis, is formulated to indicate that there is a difference.

The alternative hypothesis in step 1 provides a difference between specified populations or parameters. To test the two hypotheses, it is necessary to develop a test statistic that reflects the difference suggested by the alternative hypothesis. The test statistic is a random variable and has a sample distribution.

3. Level of significance

4. Data Analysis

It shows the available situations and possible decisions involved in a hypothesis test. Two types of errors are suggested: 1. Type I Error: Reject H 0 2. Type II error: Accept H when, in fact, H 0 is true. 0 when, in fact, H 0 is false.

ABefore data is collected, it is necessary to provide a probabilistic framework for accepting or rejecting the null hypothesis and subsequently making a decision. The framework should reflect the consideration to be taken into account of the random variation that can be expected in a sample of data. This chance variation is called sampling variation

Given the level of significance α, it is possible to determine the sample size required to meet any rejection criteria. The selection of the sample size is discussed in the After obtaining the necessary data section, the sample is used to calculate an estimate of the test statistic.

GENERAL PROCEDURE

The null hypothesis is rejected when the calculated value is in the rejection region. Rejection of the null hypothesis implies acceptance of the alternative hypothesis.

6. Select the appropriate hypothesis.

5. Reject Region

The decision whether or not to accept the null hypothesis depends on a comparison of the calculated value of the test statistic and the critical value.

The rejection region consists of those values of the test statistic that are unlikely to occur when the hypothesis is null is, in fact, true.

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When a calculated value of the test statistic is in the rejection region, there are two possible explanations. First, the sampling procedure may have resulted in an extreme value by pure chance. Because the probability of this event is relatively small, this explanation is most often rejected. Second, the extreme value of the test statistic may have occurred because the null hypothesis is false.

Theoretical models are available for all commonly used hypothesis tests. In cases where theoretical models are not available, approximations are usually developed.

• The level of significance, which is a primary element of the decision process in hypothesis testing, represents the probability of making a Type I error and is denoted by α. The probability of a type II error is denoted by β .

• The selection of the level of significance should be based on a rational analysis of its effect on decisions, and should be selected prior to the collection and analysis of sample data.

• The value chosen for α is often based on convention and the availability of statistical tables, and values of 0.05 and 0.01 are often selected for α

To illustrate the random variable involved, a test of a population mean when the standard deviation of the population is known involves two random variables: the sample mean and the Z statistics of the Equation. If the standard deviation of the population is not known, the values of three random variables are calculated: the sample mean, the sample standard deviation, and a calculated t-statistic.

• The region of acceptance consists of those values of the test statistic that would be expected when the null hypothesis is, in fact, true. Extreme values of the test statistic are less likely to occur when the null hypothesis is true.
• The critical value of the test statistic is defined as the value that separates the reject region from the acceptance region.