Question

What are the Type I and Type II errors? Discuss and compare

Answer 1

Type I: It is probability of rejecting the true null hypothesis.

Type II: It is probability of fail to reject the false null hypothesis.

For example:

Suppose that a study has been published linking arsenic, which is commonly found in tap water, to increased cancer rates. The study also stated that arsenic levels below 10 ppm could be considered harmless. Suppose that residents of union, NJ are worried about the arsenic level in the local tap water.

Since we want to test whether arsenic levels below 10 ppm so alternative hypothesis is

Ha : mu < 10

and null hypothesis is

H0: mu >= 10

Type I error:

Researcher incorrectly conclude that arsenic levels below 10 ppm while it is actually equal to 10 ppm or more than 10 ppm.

Type II error:

Researcher incorrectly conclude that arsenic levels is equal to 10 ppm or more than 10 ppm while it is actually below 10 ppm.