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  #1  
Old 05-18-2011
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Stats Type I and II error and Power

For each of the following situations, using statements 1 through 4, identify which is the Type I Error, Type II Error, the event of correctly rejecting the null hypothesis (Power) and the event of correctly not rejecting the null hypothesis.

Null Hypothesis: A production run of a drug is of satisfactory quality
Alternative Hypothesis: A production run of a drug is of unsatisfactory quality

Conclusions of the study:

1. Reject a run of satisfactory quality.
2. Put on the market a run of satisfactory quality.
3. Reject a run of unsatisfactory quality.
4. Put on the market a run of unsatisfactory quality.

a) Type I error
b) Type II error
c) Power
d) Correctly not rejecting the null hypothesis.
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Old 05-18-2011
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1. Type I error (rejecting null hypothesis)
2. Correctly not rejecting the null hypothesis.
3. Type II error (not rejecting null hypothesis)
4. Power
That's what i think..
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Old 05-18-2011
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My guess...

1. a) Type I error
2. d) Correctly not rejecting the null hypothesis.
3. c) Power
4. b) Type II error
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Old 05-18-2011
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1- a
2- d ?
3- c
4- b
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Old 05-19-2011
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Correct Answer The correct answers

1. Reject a run of satisfactory quality => a) Type I Error - the event that the null hypothesis is rejected when H0 is actually true

2. Put on the market a run of satisfactory quality => d) Correctly not rejecting the null hypothesis

3. Reject a run of unsatisfactory quality => c) Correctly rejecting the null hypothesis - Power

4. Put on the market a run of unsatisfactory quality => b) Type II Error - the event that the null is not rejected when the alternative is true
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can you please explain option 3 and 4 in detail. I actually didn't get it. :sorry:
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Old 05-19-2011
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Quote:
Originally Posted by struggle View Post
can you please explain option 3 and 4 in detail. I actually didn't get it. :sorry:

Null Hypothesis: A production run of a drug is of satisfactory quality
Alternative Hypothesis: A production run of a drug is of unsatisfactory quality


3. Reject a run of unsatisfactory quality => c) Power
Power = P( reject H0 | H0 NO TRUE ) = P( reject H0 | HA is TRUE )= 1 - Beta
Power = P( reject "A production run of a drug is of satisfactory quality" | "A production run of a drug is of unsatisfactory quality")
= Reject a run of unsatisfactory quality

4. Put on the market a run of unsatisfactory quality => b) Type II Error
Type II = P( not reject H0 | HA true ) = P( "accept" H0 | HA true) ** we never "accept" H0, we just reject or fail to reject it…but I wrote it like that for a better understanding
Type II = P( fail to reject "A production run of a drug is of satisfactory quality" | "A production run of a drug is of unsatisfactory quality" )
= Put on the market a run of unsatisfactory quality (we put it on the market anyway)


* P(x|y) = the probability of some event x, given the occurrence of some other event y
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