# Type 1 and type 2 errors

##### Intros
###### Lessons
1. What are type 1 and type 2 errors and how are they significant?
2. Calculating the Probability of Committing a Type 1 Error
3. Calculating the Probability of Committing a Type 2 Error
##### Examples
###### Lessons
1. Determining the Significance of Type 1 and Type 2 Errors
What are the Type 1 and Type 2 Errors of the following null hypotheses :

This table may be useful:
 $H_0$ is true $H_0$ is false Reject $H_0$ Type 1 Error (False Positive) Correct Judgment Fail to Reject $H_0$ Correct Judgment Type 2 Error (False Negative)
1. "An artificial heart valve is malfunctioning"
2. "A toy factory is producing defective toys"
3. "A newly designed car is safe to drive"
2. Calculating the probability of Committing Type 1 and Type 2 Errors
Suppose 8 independent hypothesis tests of the form $H_0:p=0.75$ and $H_1:p$ < $0.75$ were administered. Each test has a sample of 55 people and has a significance level of $\alpha$=0.025. What is the probability of incorrectly rejecting a true $H_0$ in at least one of the 8 tests?
1. Pacus claims that teachers make on average less than $66,000 a year. I collect a sample of 75 teachers and find that their sample average salary is$62,000 a year. The population standard deviation for a teacher's salary is $10,000 a year. 1. With a significance level of $\alpha$=0.01 what can we say about Pacus' claim? 2. Unbeknownst to me the actual average salary of a teacher is$61,000. What is the probability of committing a type 2 error when testing Pacus' claim?