Question

An article regarding interracial dating and marriage recently appeared in a newspaper. 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. Among Asians, 79% would welcome a white person into their families, 71% would welcome a Latino, and 66% would welcome a black person.

NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed.

Construct three 95% confidence intervals. (Round your answers to four decimal places.)

(i) Percent of all Asians who would welcome a white person into their families

(ii) Percent of all Asians who would welcome a Latino into their families.

(iii) Percent of all Asians who would welcome a black person into their families.

Answer 1

i) Sample proportion = 0.79 (sample proportion of Asians that would welcome a white person into their family)
Sample size (n) = 254
Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that

Required confidence interval = (0.79-0.0502, 0.79+0.0502)
Required confidence interval = (0.7398, 0.8402)

ii) Sample proportion = 0.71 (sample proportion of Asians that would welcome a Latino into their family)
Sample size (n) = 254
Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that

Required confidence interval = (0.71-0.0559, 0.71+0.0559)
Required confidence interval = (0.6541, 0.7659)

iii) Sample proportion = 0.66 (sample proportion of Asians that would welcome a black person into their family)
Sample size (n) = 254
Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that

Required confidence interval = (0.66-0.0582, 0.66+0.0582)
Required confidence interval = (0.6018, 0.7182)
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