Type 1 and type 2 errors

Lessons

• Introduction
  a)

  What are type 1 and type 2 errors and how are they significant?
  
  
  b)

  Calculating the Probability of Committing a Type 1 Error
  
  
  c)

  Calculating the Probability of Committing a Type 2 Error
  
  

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• 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)

  a)

  "An artificial heart valve is malfunctioning”
  
  
  b)

  "A toy factory is producing defective toys”
  
  
  c)

  “A newly designed car is safe to drive”
  
  

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• 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?

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• 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 $\alpha$=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?
  
  

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