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 1715 randomly selected adults, 314 identified themselves as Latinos, 321 identified themselves as blacks, 254 identified themselves as Asians, and 776 identified themselves as whites. In this survey, 86% of blacks said that their families would welcome a white person into their families.

Which distribution should you use for this problem? (Round your answers to four decimal places.)

a) P' ~ ___ ( ____ , ____ )

b) Construct a 95% confidence interval for the population proportion of blacks that would welcome a white person into their family.       (i) State the confidence interval. (ii) Calculate the error bound

Explanation / Answer

n= 1715, p = 776/1715 = .452

=? ± Z/2(pq/n
= .452 ± 1.96 * (.452)(.548) /1715
= .452 ± 0.7448
= 1.1968 ,-0.2928

(1.1968,-0.2928)

Calculate the error bound.

= (1.96) (.187)(.813)/1709
= 0.0184

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