Tran Holten, a quantitative analyst with Smith, Kleen & Beetchnutty Brokerage, has just been informed of an important error in one of his recent statistical endeavors. Specifically, in one hypothesis test, Mr. Holten rejected a null hypothesis that later was proven to be true. Which of the following best describes this type of error in hypothesis testing? Further, if the confidence level of the test were increased, would the probability of this error increase, decrease, or remain unchanged?

Explanation: In this example, Tran Holten has incorrectly rejected a null hypothesis. This type of error in hypothesis testing is called a Type I error. In hypothesis testing, the Type I error is given much more attention than the Type II error. In most hypothesis tests, the probability of a null hypothesis is equal to the significance level of the test. A significance level of 0.01, for example, indicates that a 1% chance exists that the null hypothesis will be rejected when it is indeed true. Another way to think of the probability of a Type I error is to observe the following relationship: {Probability of a Type I error = (1 - confidence level)}.

For example, a confidence level of 95% leaves a 5% probability of a Type I error occurring. If this confidence level were to increase to say, 98%, then the probability of a Type I error would reduce to 2%. As you can see, there is a relationship between the confidence level of a test and the probability of a Type I error. If the confidence level of the test in this example were to increase, then the probability of a Type I error would decrease.