An article regarding interracial dating and marriage recently appeared in a news

Question

An article regarding interracial dating and marriage recently appeared in a newspaper. Of the 1706 randomly selected adults, 312 identified themselves as Latinos, 324 identified themselves as blacks, 255 identified themselves as Asians, and 775 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. (In general, you must first prove that assumption, though.)

Part (a) Construct the 95% confidence intervals for the three Asian responses. (Round your answers to four decimal places.)

Explanation / Answer

Solution:

Construct a 95% confidence interval

n = 1706, p = 324/1706 = 0.189

= x ± Z/2 * (pq/n)
= 0.189 + 1.96 * (0.189)(0.811) /1706
= 0.189 + 0.0186
= 0.2076

= 0.189 - 1.96 * (0.189)(0.811) /1706
= 0.189 - 0.0186
= 0.1704

(0.2076, 0.1704)

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