Answer the following problems showing your work and explaining (or analyzing) your results. 1. Explain Type I and Type II errors. Use an example if needed.
Type I errors, also known as an error of the first kind involves the rejection of a true null hypothesis that is actually the equivalent to a false positive. If the null hypothesis is rejected, a statement can be made that the control does in fact have some effect on the test. But if the null hypothesis is true, then in reality the control does not fight the test in any way visible. Although, type I errors can be controlled, the value of alpha is related to the level of importance that are selected as a direct bearing on type I errors. Alpha is the maximum probability that there will be a type I error. If the value of alpha is 0.05 this equates to a 95% confidence level. Meaning there is a 5% probability that a true null hypothesis will be excluded. In the long run, one out of every twenty hypothesis tests performed at this level will result in a type I error. (www.statistics.about.com, 2014). Type II error, also known as a "false negative": the error of not rejecting a null hypothesis when the alternative hypothesis is the true state of nature. In other words, this is the error of failing to accept an alternative hypothesis when you don't have adequate power. Plainly speaking, it occurs when we are failing to observe a difference when in truth there is one. So the probability of making a type II error in a test with rejection region R is 1 (is true) a − P R H. The power of the test can be (is true) a P R H. (www.stat.berkeley.edu,
