Question

An agency claims that the mean age of bus drivers in Chicago is no more than 42 years. A hypothesis test is performed. Identify type 1 & 2 errors.   

Answer 1

Solution:

For the given hypothesis test scenario, we have

Null hypothesis: H0: The mean age of bus drivers in Chicago is no more than 42 years.

Alternative hypothesis: Ha: The mean age of bus drivers in Chicago is more than 42 years.

H0: µ ≤ 42 versus Ha: µ > 42

Type I error is occurred when we reject the null hypothesis when it is true.

In context of this problem, the type I error occurred when we conclude that the mean age of bus drivers in Chicago is more than 42 years, however, in fact, mean age of bus drivers in Chicago is no more than 42 years.

Type II error is occurred when we do not reject the null hypothesis when it is not true.

In context of this problem, the type II error occurred when we conclude that the mean age of bus drivers in Chicago is no more than 42 years, however, in fact, mean age of bus drivers in Chicago is more than 42 years.