Null hypothesis

The null hypothesis, which is symbolically expressed as H0, is a statement that indicates no difference between a parameter and a specific value or between two parameters.

Alternative Hypothesis

The alternative hypothesis, which is symbolically expressed as HA or H1, is a statement that indicates the presence of a difference between a parameter and a specific value or between two parameters.

Decision Rules

On testing the null hypothesis, two main decision rules are plausible. These decisions are arrived at using either the critical value or the probability value (p-value). On one hand, the critical value is a value that indicates the boundary between the critical region and the non-critical region. In this case, the critical region is a range of values of the test statistic that denotes a significant difference and that the null hypothesis should be rejected. On the other hand, the p-value denotes the likelihood of obtaining an extreme sample statistic when the null hypothesis is true. In this case, we may reject the null hypothesis or fail to

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For instance when testing the null hypothesis H0: the performance of male students in science and mathematics is similar to that of female students, a researcher might reject the null when it is true. In this case, the researcher would conclude that the performance of male students in science and mathematics is different from that of female students while it is false.

Type II Error

Type II error is an error that arises when a researcher accepts a false null hypothesis. For instance, in testing the null hypothesis H0: the rate of unemployment in country A is the same as that in country B, a researcher would accept H0 when it is false. Instead, the researcher would have rejected the null and accepted the alternative H1: the rate of unemployment in country A is greater than that in country