Significance Tests and Decision Making Statistics and Probability with Applications 3 rd Edition Starnes amp Tabor Bedford Freeman Worth Publishers Significance Tests and Decision Making Learning Targets ID: 1047194
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1. Testing a ClaimLesson 8.2Significance Tests and Decision MakingStatistics and Probability with Applications, 3rd EditionStarnes & TaborBedford Freeman Worth Publishers
2. Significance Tests and Decision MakingLearning TargetsAfter this lesson, you should be able to:Determine if the results of a study are statistically significant and make an appropriate conclusion using a significance level.Interpret a Type I error and a Type II error in context.Give a consequence of a Type I error and a Type II error in a given setting.
3. Significance Tests and Decision MakingThere are two types of conclusions you can make in a significance test: P-value small →Reject H0 → Convincing evidence for H a (in context)P-value large → Fail to reject H0 → Not convincing evidence for H a (in context)To determine if a P-value should be considered small, we compare it to a boundary value called the significance level. We denote it by α, the Greek letter alpha.Significance LevelThe significance level α is the value that we use as a cutoff to decide if an observed result is unlikely to happen by chance alone when the null hypothesis is true.
4. Significance Tests and Decision MakingWhen our P-value is less than the chosen significance level α in a significance test, we say that the result is “statistically significant at the α = ___ level.” In that case, we reject the null hypothesis H0 and conclude that there is convincing evidence in favor of the alternative hypothesis H a.How to Make a Conclusion in a Significance TestIf P-value < α :Reject H0 and conclude that there is convincing evidence for H a (in context).If P-value ≥ α :Fail to reject H0 and conclude that there is not convincing evidence for H a (in context).
5. Significance Tests and Decision MakingWhen we draw a conclusion from a significance test, we hope our conclusion will be correct. But sometimes it will be wrong. There are two types of errors we can make: a Type I error or a Type II error.Type I Error, Type II ErrorA Type I error occurs if a test rejects H0 when H0 is true. That is, the test finds convincing evidence that H a is true when it really isn’t.A Type II error occurs if a test fails to reject H0 when H a is true. That is, the test does not find convincing evidence that H a is true when it really is.
6. Significance Tests and Decision MakingTruth about the populationH0 trueTruth about the populationH a trueConclusion based on sampleReject H0Type I errorCorrect conclusionConclusion based on sampleFail to reject H0Correct conclusionType II errorIf H0 is true:• Our conclusion is correct if we don’t find convincing evidence that H a is true.• We make a Type I error if we find convincing evidence that H a is true.If H a is true:• Our conclusion is correct if we find convincing evidence that H a is true.• We make a Type II error if we do not find convincing evidence that H a is true.
7. Significance Tests and Decision MakingThe most common significance levels are ɑ = 0.05, ɑ = 0.01, and ɑ = 0.10. Which is the best choice for a given significance test? That depends on whether a Type I error or a Type II error is more serious.Determining Type I Error ProbabilityThe probability of making a Type I error in a statistical test is equal to the significance level ɑ.
8. LESSON APP 8.2Are these potatoes keepers?A company that makes potato chips requires each shipment of potatoes to meet certain quality standards. If the company finds convincing evidence that more than 8% of the potatoes in the shipment have “blemishes,” the truck will be sent back to the supplier to get another load of potatoes. Otherwise, the entire truckload will be used to make potato chips. The producer will perform a significance test using the hypothesesH0 : p =0.08 Ha : p > 0.08where is the true proportion of potatoes with blemishes in a given truckload.
9. LESSON APP 8.2Are these potatoes keepers?A supervisor selects a random sample of 500 potatoes from the truck and finds that 52 of the potatoes ( = 0.104) have blemishes. The resulting P-value of the test is 0.0240.What conclusion should the supervisor make at ɑ = 0.05?Describe a Type I and a Type II error in context.Give a consequence of each type of error in this setting. Which error is more serious for the potato chip producer? Explain.Based on your answer to Question 3, do you agree with the producer’s choice of ɑ = 0.05? Why or why not?
10. Significance Tests and Decision MakingLearning TargetsAfter this lesson, you should be able to:Determine if the results of a study are statistically significant and make an appropriate conclusion using a significance level.Interpret a Type I error and a Type II error in context.Give a consequence of a Type I error and a Type II error in a given setting.Lesson 8.2 Seatwork/HomeworkPg. 512 #1, 2, 5, 8, 9, & 12Seatwork/Homework: