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# 8.3 critical region

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### 8.3 critical region

1. 1. AP/H StatisticsMrs. LeBlanc – Perrone Name: ______________________________ 8.3: Critical RegionGuided Notes Date: ___________8.3 Testing a Proportion Using Critical Regions Testing a Proportion Using Critical Regions o To test a proportion using critical regions, we will use a similar process to those for testing the mean (8.1 & 8.2) o The main difference is that we are working with a _____________________________________ o When using the critical region method, we check if the sample test statistic falls in the critical region.  If it _________, we ___________  If it _______________, then we ________________  Recall that when using critical regions, the ________________________ of the sketch is  Since the distribution is _______________________________________ we find the critical values using invNorm 1
2. 2. AP/H StatisticsMrs. LeBlanc – Perrone How to Test 1. ________________________________________________________________________ Is this a binomial experiment with trials? Does represent the probability of success? Identify Is the sample large? (Is and ?) (Use p from ) If yes, then the distribution can be approximated by the normal distribution 2. ________________________________________________________________________ ________________________________________________________________________ 3. ________________________________________________________________________ Test Statistic: 4. ________________________________________________________________________ The area of the critical region = 5. Conclude the test __________________________________________________________________ __________________________________________________________________ 6. Interpret the results in the context of the application 2
3. 3. AP/H StatisticsMrs. LeBlanc – Perrone EXAMPLE: Testing , Critical Regions A botanist has produced a new variety of hybrid wheat that is better able to withstand drought than other varieties. The botanist knows that for the parent plants, the proportion of seeds germinating is 80%. The proportion of seeds germinating for the hybrid variety is unknown, but the botanist claims that it is 80%. To test this claim, 400 seeds from the hybrid plant are tested, and it is found that 312 germinate. Use a 5% level of significance to test the claim that the proportion germinating for the hybrid is 80%. 3
4. 4. AP/H StatisticsMrs. LeBlanc – PerroneSummary Questions 1. How is testing (using critical values) similar to testing (using critical values)? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. When testing using critical values, what is the test statistic for? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________“HOT” Question:____________________________________________________________________________________________________________________________________________________________________________________ 4