Power of a Test

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Power of a Test
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Remember

• Type I error Reject the H0 when you
  shouldnt have.
• Type II error - Fail to reject the Ho when
  you should have.

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Fill in the chart with the type of error
Null is True Null is False
Reject Null    
Fail to Reject Null    
By choosing a level of significance ( ) we
determine the probability of committing a type I
error.
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Power of a Test (1 ß)

• It measures the sensitivity of the test to detect
  a real difference in parameters if one really
  exists.
• Rejecting a False Ho.

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• To increase the power of a test we
• Increase alpha
• Use a larger sample size.

Null is True Null is False
Reject Null  Type I error (a) Correct decision (1-ß)
Fail to Reject Null  Correct decision (1-a)  Type II error (ß)
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Cigarette manufacturer claims that the mean
nicotine content of its cigarettes is 1.5 mg.
Researchers believe its more than this. Test a
sample of 36 and find standard deviation is 0.2.
Use a 1 significance level. (Suppose its really
1.6)
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A study claims that the mean weight of a book is
2.4 pounds. Researchers believe that it is more.
Test a sample of 30 and st. dev. Is 0.5 pounds.
Use 5 significance level. (What if its really
2.7 pounds?)
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A study claims that the mean weight of a dog is
26.8 pounds. Researchers believe that its less
than this. Test a sample of 36 and st. dev. Is
2.2 pounds. Use 5 significance level. (What if
its really 26 pounds?)
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Homework

• Worksheet