Two Proportions Notes Spring - 2 of 9 Question 2 What do we...

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2 of91.1 IntroductionQuestion2.What do we want to test?REVIEWWhat is a hypothesis test?
a.Eight simple steps0. Write down what isknown.1. Determine which type of hypothesistestto use.2. Check the test’srequirements.3. Formulate thehypothesis:H0,Ha4. Determine thesignificance levelα.5. Find thep-value.6. Make thedecision.7. State the finalconclusion.
Question3.What is a test statistic?Question4.What is the test statistic’s distribution based on?
Anthony TanbakuchiMAT167
Question5.What is thep-value?Question6.If we rejectH0what is the probability of a Type I error?Question7.When does a Type II error occur?Question8.What variable represents the probability of a Type II error?1.2Testing claims about 2 population proportionsUSEOften used to help answer:1. Is the proportion ofxthe same in the two populations?2. Is the proportion ofxthe 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?COMPUTATIONNotationSince we havetwo samples(sample 1 & sample 2) we can define the numberof successes, the sample size, and estimates ofpin terms of each sample:successes:x1, x2(2)Anthony TanbakuchiMAT167
4 of91.2 Testing claims about 2 population proportionssample sizes:n1, n2(3)point estimate:ˆp1=x1n1,ˆp2=x2n2,Δˆp= ˆp1-ˆp2(4)And make hypothesis about the two populations:population parameters:p1, p2Δp=p1-p2(5)Dependent vs. independent samplesIndependent samples.Definition 1.1The samples from one population are not related to or paired with thesamples values in from the other population.

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