How to tackle a Type II error homework Question

Type II Error

  Image Source

In Hypothesis testing, there are two types of errors that can occur. They are Type I error and Type II error. Type I error is the probability of erroneously rejecting the null hypothesis. That means, reject the null hypothesis when it is true. Type II error is  the probability of erroneously accepting the null hypothesis. That means, do not reject the null hypothesis when it is false.

Here is an example of how to tackle a question which deals type II error.

(Question) A study is done to see if the average age a ‘child’ moves permanently out of his parents’ home in the United States is at most 23. 43 U.S Adults, all age 40, were surveyed. Then sample average age was 24.2 with a standard deviation of 3.7. Which is the type II error?

• Conclude that the average age is greater than 23, when it is at most 23.
• Conclude that the average age is greater than 23, when it is 24.2
• Conclude that the average age is at most 24.2, when it is at most 24.2
•       Conclude that the average age is at most 23, when it is greater than 23

(Explanation) Type II error is the probability that not rejecting the null hypothesis when it is false. Here the null hypothesis is that the average age a ‘child’ moves permanently out of his parents’ home in the United States is at most 23. So type II error would be  concluding that the average age is at most 23 (not rejecting the null hypothesis) when it is greater than 23 (when it is false). So the correct answer is the last option.