Question

Explain why there is an inverse relationship between committing a Type I error and committing a Type II error. What is the best way to reduce both kinds of error?

Answer 1

Type I error is an error in which the null hypothesis is rejected even when it is true.Type II error is an error in which the null hypothesis is accepted even when it is false.

A Type I error is often represented by the alpha (?) and a Type II error by the beta (? ). In choosing a level of probability for a test, is basically we are actually deciding how much we want to risk committing a Type I error—rejecting the null hypothesis when it is, true. For this reason, the area in the region of rejection is sometimes called the alpha level because it shows the likelihood of committing a Type I error.

In order to discuss a Type II, or ?, error, it is necessary to imagine next to the distribution for the null hypothesis a second distribution for the true alternative. If the alternative hypothesis is actually true, but we fail to reject the null hypothesis for all values of the test statistic falling to the left of the critical value, then the area of the curve of the alternative (true) hypothesis lying to the left of the critical value represents the percentage of times that you will have made a Type II error.( See the Picture).

Type I and Type II errors are inversely related: As one increases, the other decreases.

The best way to reduce both kinds of error :

• Increase the sample size
• If level of significance reduces from 5 to 1% than the rejection area also reduces thus lower rejection area reduces the chances that points will fall out of a population in this rejection area and thus less the probability of incorrectly identifying true samples in the rejection area.