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Type 1 and type 2 errors
- Intro Lesson: a9:54
- Intro Lesson: b6:51
- Intro Lesson: c3:18
- Lesson: 1a6:48
- Lesson: 1b5:17
- Lesson: 1c5:37
- Lesson: 27:17
- Lesson: 3a9:51
- Lesson: 3b18:38
Type 1 and type 2 errors
Lessons
A type 1 error is the probability of rejecting a true H0.
α=P(reject H0∣True H0)
So in this case our hypothesis test will reject what is a true H0.
Type 2 Errors:
A type 2 error is the probability of failing to reject a false H0.
β=P(Failing to Reject H0∣False H0)
|
H0 is true |
H0 is false |
Reject H0 |
Type 1 Error (False Positive) |
Correct Judgment |
Fail to Reject H0 |
Correct Judgment |
Type 2 Error (False Negative) |
The Power of a Hypothesis Test is the probability of rejecting H0 when it is false. So,
Power =P(Reject ∣H0 is false)=1−P(Fail to Reject ∣H0 is false)=1−β
Recall:
Test Statistic:
Proportion: Z=np(1−p)p^−p
Mean: Z=nσx−μ
- Introductiona)What are type 1 and type 2 errors and how are they significant?b)Calculating the Probability of Committing a Type 1 Errorc)Calculating the Probability of Committing a Type 2 Error
- 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:
H0 is true
H0 is false
Reject H0
Type 1 Error (False Positive)
Correct Judgment
Fail to Reject H0
Correct Judgment
Type 2 Error (False Negative)
a)"An artificial heart valve is malfunctioning"b)"A toy factory is producing defective toys"c)"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 H0:p=0.75 and H1:p < 0.75 were administered. Each test has a sample of 55 people and has a significance level of α=0.025. What is the probability of incorrectly rejecting a true H0 in at least one of the 8 tests? - 3.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.a)With a significance level of α=0.01 what can we say about Pacus' claim?b)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?