Two Proportions Notes Spring

Two Proportions Notes Spring - 2 of 9 1.1 Introduction...

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Unformatted text preview: 2 of 9 1.1 Introduction Question 2 . What do we want to test? REVIEW What is a hypothesis test? A hypothesis test calculates the probability of observing our sample data as- suming the null hypotheses H is true . If the probability is low enough ( p-value ≤ α ), we reject H and have evidence to support our alternative hy- pothesis H a . Eight simple steps 0. Write down what is known . 1. Determine which type of hypothesis test to use. 2. Check the test’s requirements . 3. Formulate the hypothesis : H , H a 4. Determine the significance level α . 5. Find the p-value . 6. Make the decision . 7. State the final conclusion . K-T-R-H-S-P-D-C: “Know The Right Hypothesis So People Don’t Com- plain” Question 3 . What is a test statistic? Question 4 . What is the test statistic’s distribution based on? Common form of a test statistic Anthony Tanbakuchi MAT167 Testing a claim about two proportions 3 of 9 test statistic = (sample statistic)- (null hypothesis of parameter) (standard deviation of sample statistic) (1) Question 5 . What is the p-value? Question 6 . If we reject H what is the probability of a Type I error? Question 7 . When does a Type II error occur? Question 8 . What variable represents the probability of a Type II error? 1.2 Testing claims about 2 population proportions USE Often used to help answer: 1. Is the proportion of x the same in the two populations? 2. Is the proportion of x the same in the two populations? 3. Is process 1 equivalent to process 2? (Produces same proportion.) 4. Is the new process better than the current process? (Has a higher yield.) 5. Is the new process better than the current process by at least some pre- determined threshold amount? COMPUTATION Notation Since we have two samples (sample 1 & sample 2) we can define the number of successes, the sample size, and estimates of p in terms of each sample: successes: x 1 ,x 2 (2) Anthony Tanbakuchi MAT167 4 of 9 1.2 Testing claims about 2 population proportions sample sizes: n 1 ,n 2 (3) point estimate: ˆ p 1 = x 1 n 1 , ˆ p 2 = x 2 n 2 , Δˆ p = ˆ p 1- ˆ p 2 (4) And make hypothesis about the two populations: population parameters: p 1 ,p 2 Δ p = p 1- p 2 (5) Dependent vs. independent samples Independent samples. Definition 1.1 The samples from one population are not related to or paired with the samples values in from the other population.samples values in from the other population....
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Two Proportions Notes Spring - 2 of 9 1.1 Introduction...

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