Death Penalty Study: In October 2008, the Gallup Poll asked 510 randomly sampled

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Death Penalty Study: In October 2008, the Gallup Poll asked 510 randomly sampled adults the question Generally speaking,de you believe the death penalty is applied fairly or unfairly in this country today? of these, 275 adults answered Fairly," 194 adults said "Unfairly, and 41 adults said they didn't know For this project, use StetCrench to: One sample proportion summary hypothesis test: Ho:p-0.5 HA : p0.5 reference: http://www.gallup.com/poll/1605/death-penalty aspx) Hypothesis test results Proportion Count Total Sample Prop.Std. Err Z-Stat P-value 1. Test the researcher's claim that more than half of American adults believe the death penalty is applied fairly using a significance level of 0.05 275 510 0.53921569 0.022140372 17712298 0.0383 STATCRUNCH DIRECTIONS FOR PROPORTION HYPOTHESIS TEST: Cliek os Stet > Proportion P value 0.0383 One Somple > with Summary > Enter in the number of "successes. ond the totor number or observations. Then click on Hypothesis Test for p and in the hypothesized value and correct symbol for the akernative bypothesis Clfick Compute. Probability or chance of getting a p(hat) 0.54 (275/510), while assuming the true value of p is 0.0383 (1-0.54) is only .0383. Conclusion Support Ha, we have enough evidence to support the claim that more than half of American adults belleve the death penalty is applied fairly Assumptions are met. The sample is random and n-510>30 a. b. -Copy and paste the output into your document. Then answer the following questions 1. Interpret the p-value. What is the initial deeision 2. State the conclusion of your hypothesis test. 3. Verily the assumptions are met to use this method c. One sample proportion summary confidence interval: Method: Standard-Wald 90% confidence interval results: Proportion Count Total Sample Prop.Std. Err. L.Limit 2. Generate a 90% confidence interval to estimate the proportion of adults that believe the death penalty is applied fairly in this country, .STATCRUNCH DIRECTIONS FOR PROPORTION CONFIDENCE INTERVAL: Cck oe Stet Proportion Stats> One Sample With Summary>Enter in the number of "successes and the total number of observations. Then click on confidence interval for p and in your confidence level> Ciek Compute. : Copyand paste the output into your document. Then answer the follawing questions: U. Limit 275 510 0.53921569 0.022072169 0.5029102 0.57552117 2. 1. Interpret the confidence interval 2. Does your confidence interval support your hypothesis test conclusion? am 90% confident the true mean proportion of adults that believe the death penalty is applied fairly in this country is between 0.5029 0.5755 Yes, the confidence interval does support our hypothesis test conclusion, Our hypothesis was the claim that more than half of American adults belleve the death penalty is applied fairly. Our minimum 90% confidence interval is 50.3% and our max limit is 57.6%, the limits support our claim because the lower limit is just barely above 50%. a. Explain. b. 6 pts Pts

Explanation / Answer

For one sample test the test statistic is given by z=(sample proportion-hypothesized proportion)/(standared error of the sample),here it will be=((275/510)-0.5)/0.022140372=(0.53921569-0.5)/0.022140372=1.7712298,which has p-value 0.0383<0.1.So,with 10% level of significance we fail to reject H0 we conclude that the population proportion correspondinf to the partiular level["fairly"] is 0.5

[P.S. How to calculates standard error:-

The hypothesized population proportion is 0.5,the sample size is=510,so hypothesized variance of population propotion[from sampling theory result] is=p*(1-p)/510=(0.5*(1-0.5)/510= 0.0004901961,So,hypothesized standard error of the sample is=sqrt{0.0004901961}=0.022140372]

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