Under what conditions would you use a t-test as opposed to a z-test? Can you use the t-table to determine the critical value of the z-test? Explain why. What are the differences between a one-tailed and a two-tailed test? What is the importance of a 5% significance level? Why would you choose 5% as opposed to 10% or 1%? What effect does the level of significance have on a Type II error?
1a It is certain that the level of significance may, in some cases, determine whether our null hypothesis will be accepted or not. Our E-Text states the following “… Thus, there is a possibility of two types of error—a Type I error, wherein the null hypothesis is rejected when it should have been accepted, and a Type II error, wherein the null hypothesis is not rejected when it should have been rejected”. Many statisticians use 0.05 as the default level of significance, but we are certainly free to use other levels of significance as we see fit. How would you go about choosing your level of significance? Provide an example.
1b Marvin L. Wolverton, PhD, MAI, wrote an interesting paper on tests of hypotheses: "Research Design, Hypothesis Testing, and Sampling", Appraisal Journal. Fall2009, Vol. 77 Issue 4, p370-382. 13p. 2 Diagrams. What does this author say about choosing an appropriate level of significance?
What is the difference between a left-tailed, two-tailed, and right-tailed test. When would you choose a one-tailed test? How can you determine the direction of the test by looking at a pair of hypotheses? How can you tell which direction (or no direction) to make the hypothesis by looking at the problem statement?
Why does the significance level differ among industries? Will the null hypothesis be more likely to be rejected at α = 0.01 than α = 0.10? As the significance level increases to α = 0.10 from α = 0.01, which type error is more likely to occur? What can be done to reduce the likelihood of incurring this error?