Final answer:
Hypothesis testing compares a p-value with a preconceived significance level (α) to decide on rejecting or not rejecting the null hypothesis. A decision at α = 0.05 involves comparing the p-value to 0.05 to make a decision about the null hypothesis. Conclusions are then derived based on this decision, indicating either sufficient or insufficient evidence to support the alternative hypothesis.
Step-by-step explanation:
When a student asks about the decision and conclusion with a given significance level (α = 0.05), they are referring to hypothesis testing in statistics. This involves comparing a p-value obtained from a statistical test to the preconceived α level to make a decision about the null hypothesis. If the p-value is less than or equal to α, we reject the null hypothesis. Conversely, if the p-value is greater than α, we do not reject it.
At α = 0.05, if a student states a decision to reject the null hypothesis, the reason for this decision is typically because the p-value is less than 0.05. The corresponding conclusion would be that there is sufficient evidence at the 5 percent significance level to support the alternative hypothesis proposed in their study. An example conclusion could be "There is sufficient evidence to conclude that the mean cost of auto insurance for teenage boys is greater than that for girls".
If the decision is not to reject the null hypothesis, and the p-value is greater than α, the conclusion might be that there is insufficient evidence to support the alternative hypothesis at the 5 percent significance level. For instance, "There is insufficient evidence to conclude that the standard deviation is greater than 15".