Civic Engagement The Hyde Park Neighborhood Association Outreach Committee recen

Question

Civic Engagement The Hyde Park Neighborhood Association Outreach Committee recently conducted a survey to learn more about the issues and concerns of the residents. In a random sample of 124 residents, 20 indicated that the main barrier to involvement in community events is scheduling conflicts.^30 a. Find a 90% confidence interval for the true proportion of residents who believe the main barrier to involvement in community events is scheduling conflicts. b. Suppose no prior estimate of p is known. How large a sample is necessary for the bound on the error of estimation to be 0.04 with confidence level 90%?

Explanation / Answer

a) X = 20 , n = 124 , p = X/n = 20/124 =0.1612903

z0.1 = 1.645

sqrt(p*q/n) = sqrt(20/124*104/124/124)=0.0330292

z0.1 *sqrt(p*q/n) = 0.054333

hence confidence interval is ( 0.1612903-0.054333,0.1612903+0.054333 )

= (0.106957 , 0.215623)

b) e = 0.04

n = z^2*p*q/e^2 = 1.645^2*20/124*104/124/(0.04)^2 = 228.78

= 229

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