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Significance Tests: The Basics

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1 Significance Tests: The Basics
Section 9.1 again… Significance Tests: The Basics

2 Type I and Type II Errors
If we reject 𝐻 0 when 𝐻 0 is true, we have committed a Type I error. If we fail to reject 𝐻 0 when 𝐻 0 is false, we have committed a Type II error.

3 Another way to look at it!

4 Examples If someone is on trial for murder: 𝐻 0 : 𝐻 π‘Ž :
Type I error – we reject that they are innocent when we shouldn’t have…meaning we convicted an innocent person. Type II error – we let a guilty person go free. Which is worse?

5 Examples If someone is on trial for stealing a candy bar: 𝐻 0 : 𝐻 π‘Ž :
Type I error – we reject that they are innocent when we shouldn’t have…meaning we convicted an innocent person. Type II error – we let a guilty person go free. Which is worse?

6 Put your notes on the floor.
What is Type I error? What is Type II error?

7 Example The manager of Wendy’s 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: 𝐻 0 :p=0.63 𝐻 0 :𝑝<0.63 Describe a Type I and Type II error in this setting and explain the consequences of each.

8 Significance and Type I Error
The Significance level 𝛼 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.

9 Example For a truckload of potatoes, we are testing the proportion that have blemishes. 𝐻 0 :𝑝=0.08 𝐻 0 :𝑝>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.

10 Example

11 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. π‘ƒπ‘œπ‘€π‘’π‘Ÿ=1βˆ’π›½ Power is NOT the compliment of Type I error! Beta is NOT the compliment of Type I error!

12 How are they related? 𝜢 𝜷 Power

13 Potatoes The potato-chip producer wonders whether the significance test of 𝐻 0 :𝑝= .08 vs. 𝐻 π‘Ž :𝑝>.08 based on a random sample of 500 potatoes has enough power to detect a shipment of 11% blemished potatoes.

14

15 Homework Pg. 547 (19-25, 27-30)

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