If the alpha level is changed from a=.05 to a=.01.
a. What happens to the boundaries for the critical region?
b. What happens to the probability of a Type I error?
a. They are further away from the mean.
b. It decreases proportionately.
a. When the alpha level is changed from a=.05 to a=.01, the boundaries for the critical region become more stringent. The critical region represents the values of the test statistic where the null hypothesis is rejected. A smaller alpha level means that the critical region will be smaller and more concentrated around the center of the distribution. In other words, it becomes more difficult to reject the null hypothesis.
To find the critical region boundaries, you first need to determine the critical values associated with the new alpha level of a=.01. This can be done by looking up the critical values in a statistical table or using statistical software. The critical values will depend on factors such as the distribution being used and the type of test (e.g., one-tailed or two-tailed). Once you have the critical values, you can then identify the corresponding region as the critical region.
b. The probability of a Type I error, also known as the significance level or alpha level, is directly related to the boundaries of the critical region. When the alpha level is changed from a=.05 to a=.01, the probability of a Type I error decreases.
Type I error occurs when the null hypothesis is incorrectly rejected, i.e., concluding that there is a significant effect or difference when there is actually none. By lowering the alpha level, you are reducing the threshold for rejecting the null hypothesis. This means that to reject the null hypothesis, stronger evidence is required, resulting in a lower probability of mistakenly rejecting the null hypothesis.
To calculate the probability of a Type I error, you would need to know the z-score or t-score critical values associated with the new alpha level of a=.01 and the specific test you are conducting. These critical values can be obtained from a statistical table or using statistical software. Once you have the critical values, you can compare them to the calculated test statistic to determine whether to reject the null hypothesis or not. The probability of a Type I error is equal to the alpha level.
a. When the alpha level is changed from a=0.05 to a=0.01, the boundaries for the critical region become more stringent or stricter. This means that the critical region, where you reject the null hypothesis, will be smaller and more difficult to achieve.
b. The probability of a Type I error is reduced when the alpha level is decreased from 0.05 to 0.01. Type I error refers to wrongly rejecting the null hypothesis when it is actually true. By lowering the alpha level, you are decreasing the likelihood of making this type of error. Therefore, the probability of making a Type I error decreases when the alpha level is reduced.