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Significance Tests: The Basics
Section 9.1 again⦠Significance Tests: The Basics
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Type I and Type II Errors
If we reject π» 0 when π» 0 is true, we have committed a Type I error. If we fail to reject π» 0 when π» 0 is false, we have committed a Type II error.
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Another way to look at it!
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Examples If someone is on trial for murder: π» 0 : π» π :
Type I error β we reject that they are innocent when we shouldnβt haveβ¦meaning we convicted an innocent person. Type II error β we let a guilty person go free. Which is worse?
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Examples If someone is on trial for stealing a candy bar: π» 0 : π» π :
Type I error β we reject that they are innocent when we shouldnβt haveβ¦meaning we convicted an innocent person. Type II error β we let a guilty person go free. Which is worse?
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Put your notes on the floor.
What is Type I error? What is Type II error?
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Example The manager of Wendyβs wants to reduce the proportion of drive-through customers who have to wait more than two minutes on their order. Based on store records, the proportion is currently p=0.63. To reduce this proportion, the manager assigns an additional employee to assist with drive-through orders. During the next month, the manager will collect a random sample of drive-through times and test the hypotheses: π» 0 :p=0.63 π» 0 :π<0.63 Describe a Type I and Type II error in this setting and explain the consequences of each.
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Significance and Type I Error
The Significance level πΌ of any fixed level test is the probability of a Type 1 error. If given the chance, consider the consequences of a Type I error before choosing a significance level.
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Example For a truckload of potatoes, we are testing the proportion that have blemishes. π» 0 :π=0.08 π» 0 :π>0.08 Suppose that the potato-chip producer decides to carry out this test on a SRS of 500 potatoes using a 5% significant level.
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Example
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Power and Type II Error The power of a test against any alternative is one minus the probability of a Type II error for that alternative. πππ€ππ=1βπ½ Power is NOT the compliment of Type I error! Beta is NOT the compliment of Type I error!
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How are they related? πΆ π· Power
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Potatoes The potato-chip producer wonders whether the significance test of π» 0 :π= .08 vs. π» π :π>.08 based on a random sample of 500 potatoes has enough power to detect a shipment of 11% blemished potatoes.
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Homework Pg. 547 (19-25, 27-30)
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