Question

An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the 1,709 randomly selected adults, 315 identified themselves as Latinos, 323 identified themselves as blacks, 254 identified themselves as Asians, and 779 identified themselves as whites. In this survey, 86% of blacks said that they would welcome a white person into their families. Among Asians, 77% would welcome a white person into their families, 71% would welcome a Latino, and 66% would welcome a black person. Construct a 95% confidence interval for the percent of all black adults who would welcome a white person into their families. What is the lower bound? (Round to 4 decimal places) Construct a 95% confidence interval for the percent of all black adults who would welcome a white person into their families. What is the upper bound? (Round to 4 decimal places) Construct a 95% confidence interval for the percent of all black adults who would welcome a white person into their families. What is the error bound? (Round to 4 decimal places

Answer 1

sample proportion, = 0.77
sample size, n = 779
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.77 * (1 - 0.77)/779) = 0.0151

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0151
ME = 0.0296

sample proportion, = 0.77
sample size, n = 779
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.77 * (1 - 0.77)/779) = 0.0151

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0151
ME = 0.0296

CI = (0.77 - 1.96 * 0.0151 , 0.77 + 1.96 * 0.0151)
CI = (0.7404 , 0.7996)

Lower Bound = 0.7404
Upper Bound = 0.7996

Error Bound = 0.0296

CI = (0.77 - 1.96 * 0.0151 , 0.77 + 1.96 * 0.0151)
CI = (0.7404 , 0.7996)

Lower Bound = 0.7404
Upper Bound = 0.7996

Error Bound = 0.0296