Answer to Question #212797 in Statistics and Probability for Jhay

Question

If you are to conduct a test of hypothesis, what are your considerations on the type of statistic to be used? Why?

Answer 1

If you are to conduct a test of hypothesis, what are your considerations on the type of statistic to be used? Why?

• The sample size (n) of the statistic. We anticipate that larger samples will produce more reliable results, while small samples will frequently leave the null hypothesis unquestioned. When the difference sought is minor and the population variation is high, large samples may be justifiable and suitable. Established statistical processes aid in ensuring suitable sample sizes, allowing us to reject the null hypothesis not just statistically, but also practically. These approaches must take into account the amount of type I and type II mistakes, as well as population variance and effect size.
• Level of significance ($\alpha$ ) of the statistic. When the null hypothesis is true, the significance level, also known as $\alpha$ is the chance of rejecting it. A significance level of 0.05, for example, represents a 5% chance of finding that a difference exists when there is none. Because of their technical character, these definitions can be difficult to comprehend. The concepts are much easier to understand when they are represented by a picture. The significance level specifies how far away from the null hypothesis value we will draw the line on the graph. To plot a significance level of 0.05, we must shade the 5% of the distribution that is farthest away from the null hypothesis.