Hypothesis Testing

The method in which the samples are selected to learn more about characteristics of the given population is called hypothesis testing. In other words, a systemic way to test the claims or hypothesis about a group or population parameter based on the sample data is called Hypothesis testing. In this method, one can test some hypothesis by finding the probability / likelihood that a sample statistic could have been selected, if the assumption about the population parameter is true.

**Example:** Suppose a newspaper was reported that College students in the United States spending an average of 5 hours per week on Facebook. In order to test whether this claim is true, we randomly selects 30 College students in the United States and the time (in hours) they spent on Facebook was recorded. The mean time (in hours) that we measure for these 30 students is a sample mean. With the sample mean and the population parameters, we can compare the sample mean with the corresponding population mean (stated in the newspaper article) by the use of the method of hypothesis testing.
The method of hypothesis testing can be summarized in four steps as follows:

**Step 1:**State the hypothesis**Step 2:**Construct the criteria (critical region) for a decision to be made**Step 3:**Calculate the appropriate Test Statistic**Step 4:**Make a decision based on the value of test statistic compared with the critical region.

In the first step, the hypothesis (null and alternative) has to be stated to test the proposed population parameter and it includes two hypothesis, namely null hypothesis H0 and alternative hypothesis H1. The value of the population parameter is always stated under the null hypothesis, while the statement that is opposite to the null hypothesis can be stated in an alternative hypothesis.

For example, the hypothesis to test the population mean (µ = 5 hours) can be stated as follows:

- H0: µ = 5 hours
- H1: µ ≠ 5 hours (Two-tailed test)

In the above, the alternative hypothesis states that the test is of two-tailed test. However, the alternative hypothesis can also be stated for one-tailed test in two different ways as follows:

- H1: µ > 5 hours (Right-tailed test) or
- H1: µ < 5 hours (Left-tailed test)

The critical region can be determined based on the test statistic that is appropriate for the present situation. After find the value of the test statistic, it can be compared to the critical value / critical region and to confirm whether the value of the test statistic lies in the critical region. The null hypothesis will be rejected if the value of the test statistic lies in the critical region, otherwise not.

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