Explain the difference between statistical significance and practical significance. Choose the correct answer below. A. Statistical significance refers to the type of hypothesis test needed to analyze a population, with some tests being more important than $\mathrm{Z}$ tests. Practical significance refers to how difficult a desired hypothesis test is to perform in an application, with some tests being easier to perform than others. B. Statistical significance means that the hypothesis test being performed is useful for building theoretical foundations for other statistical work. Practical significance means that the particular application of the hypothesis test is of great importance to the real world. C. Statistical significance means that the sample statistic is not likely to come from the population whose parameter is stated in the null hypothesis. Practical significance refers to whether the difference between the sample statistic and the parameter stated in the null hypothesis is large enough to be considered important in an application. D. Statistical significance refers to how an unusual event is unlikely to actually appear in a real world application, such as every entry in a sample of size 50 having the same value. Practical significance refers to how an unusual event is likely to actually appear in a real world application, such as a rejection of a null hypothesis using data that looks feasible.
Solution
Step 1 ：Statistical significance refers to the likelihood that the results observed in a study occurred by chance. If a result is statistically significant, it means that it is very unlikely to have occurred by chance alone, suggesting that there is a relationship between the variables being studied.
Step 2 ：Practical significance refers to the relevance or usefulness of that result in the real world. A result can be statistically significant but not practically significant if the difference or relationship, while statistically unlikely to have occurred by chance, is too small to be of any real-world use or interest.
Step 3 ：Looking at the options provided, option C seems to capture these definitions accurately.
Step 4 ：Final Answer: \boxed{\text{C}}. Statistical significance means that the sample statistic is not likely to come from the population whose parameter is stated in the null hypothesis. Practical significance refers to whether the difference between the sample statistic and the parameter stated in the null hypothesis is large enough to be considered important in an application.
