A Type I error occurs when a true null hypothesis is rejected. The value of(pronounced "alpha") represents the probability of committing this type of error; that is,

=P(H0 is rejected|H0 is true)

This means that ALPHA equals the Probability that H0 is rejected even if it's TRUE.

The value of represents the significance level of the test, which is the inverse of our CONFIDENCE LEVEL (that came up a few posts down). If we PICK our confidence level to be 95%, our alpha = 5% or .05.

The size of the rejection region in a statistics problem of a test of hypothesis depends on the value assigned to . In one approach to the test of hypothesis, we assign a value to before making the test. Although any value can be assigned to , commonly used values of are .01, .025, .05, and .10. Usually the value assigned to does not exceed .10 (or 10%).

Type II Error

A Type II Error occurs when a false null hypothesis is not rejected.

The value of(pronounced "Beta") represents the probability of committing a Type II error; that is,

=P(H0 is not rejected|H0 is false)

This means that BETA equals the Probability that H0 is NOT rejected even if it's FALSE.

The value of 1 is called the power of the test. It represents the probability of rejecting H0 when it is false.

Tails of the Test A two-tailed test has rejection regions in both tails, a left-tailed test has the rejection region in the left tail, and a right-tailed test has the rejection region in the right tail of the distribution curve.

What are some practical examples of a Type I error versus a Type II error? What does this look like in real life? Feel free to Google and share!