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Problem 6. A political researcher believes that the fraction p, of Republicans strongly in favor of...

Question:

Problem 6. A political researcher believes that the fraction p, of Republicans strongly in favor of the death penalty is greater than the fraction P of Democrats strongly in favor of the death penalty. He acquired independent random samples of 200 Republicans and 200 Democrats and found 46 Republicans (a) Does this evidence provide statistical support for the researchers (b) The political researcher should have designed a test for which probability o exceeds p, Pi-p,-0.10. and 34 Democrats strongly favoring the death penalty. belief? Use significance level a 0.05 by a meaningful amount. Find a common sample size n for a test with a 0.05 and B 30.20 when, in fact,
Problem 6. A political researcher believes that the fraction p, of Republicans strongly in favor of the death penalty is greater than the fraction P of Democrats strongly in favor of the death penalty. He acquired independent random samples of 200 Republicans and 200 Democrats and found 46 Republicans (a) Does this evidence provide statistical support for the researcher's (b) The political researcher should have designed a test for which probability o exceeds p, Pi-p,-0.10. and 34 Democrats strongly favoring the death penalty. belief? Use significance level a 0.05 by a meaningful amount. Find a common sample size n for a test with a 0.05 and B 30.20 when, in fact,

Answers

Since p will not be known until after we select the samplem, we need a planning value for p that can be used to make the computation Since no value for p is given, wemay use a planning value ofp* 0.5 Let us assume n, n2-n Since the two populati on proportions pi,P2 are unknown, we use the sample proportions p* = 0.5 to estimate the population proportions and so the standard error will be: A- 0.50(1-0.50)0.50(1-0.50) 0.25 0.25 a 0.05 The corresponding z-critical value is Znos-1.645 β 0.2 The corresponding z-critical value is Zo0.8416 95% confidence interval for the true difference in proportions for the data of the study is: M argin of Error 0.1 So we have (1.645 +0.8416)(0.5) 309.158978 So the sample size must be atleast 310 to acheive sucha precision That is 310 people must be included in each of the two samples

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