Compare the test statistic with the critical value. If the test statistic is greater than or equal to the critical value, we reject the null hypothesis. If it is less than the critical value, we fail to reject the null hypothesis. Step-7: Interpret the result and state the probability of making a type I or a type II error. Type I error in statistics is the probability of rejecting a hypothesis we should not have rejected. Type II error is the probability of not rejecting a hypothesis we should have rejected.
The Correct Answer and Explanation is:
In hypothesis testing, Step-6 involves comparing the calculated test statistic to the critical value (or critical region) to decide whether to reject or fail to reject the null hypothesis. The critical value is determined based on the significance level (α), which represents the probability of making a Type I error. The test statistic is the result of the sample data, such as a t-statistic, z-statistic, or chi-square statistic, depending on the test being conducted.
- If the test statistic is greater than or equal to the critical value, it means that the sample data provide enough evidence to reject the null hypothesis at the given significance level. This suggests that the alternative hypothesis is likely true.
- If the test statistic is less than the critical value, it indicates that the sample data do not provide enough evidence to reject the null hypothesis. In this case, we fail to reject the null hypothesis, meaning there is not enough support for the alternative hypothesis.
Step-7 deals with interpreting the result and considering the probabilities of making Type I and Type II errors:
- Type I error (α) occurs when we reject a true null hypothesis. In other words, we conclude that there is an effect or difference when in fact there is none. The significance level (α) is the probability of making a Type I error. For example, if α = 0.05, there is a 5% chance of rejecting a true null hypothesis.
- Type II error (β) occurs when we fail to reject a false null hypothesis. This means we do not detect an effect or difference that actually exists. The probability of a Type II error is denoted by β. Power, which is 1 − β, represents the probability of correctly rejecting a false null hypothesis.
In conclusion, Step-6 helps determine whether the null hypothesis should be rejected, while Step-7 involves assessing the risks of making errors in the decision-making process.
