Question

1. A TSA employee at an airport reviews the images of carry-on bags as they go by the x-ray machine. She is looking for dangerous material that might be carried on to a flight.

The null hypothesis is H₀: The bag does not contain any dangerous material.  

1. What is a Type-I error in this setting?
2. What is a Type-II error in this setting?

Which of the two types of error has the greater consequence?

Answer 1

Solution:

Given the null hypothesis is

H0 : The bag does not contain any dangerous material.

a) By the definition , the Type 1 error is " Rejecting H0 , when it is TRUE"

i.e. concluding that the bag contains dangerous material when it does not .

or Rejecting the bag when it does not contain any dangerous material.

b)By the definition , the Type 2 error is " Fail to Reject H0 , when it is FALSE"

i.e. concluding that the bag does not contains dangerous material when it contains some dangerous material .

or Fail to Rejecting the bag when it contains some dangerous material.

Which of the two types of error has the greater consequence?

The type 2 error has he greater consequence.