27% D Fri 9:20 PM a That I com: × 1 8 HW 120. adults, 315 as Latinos, 323 as bla

Question

27% D Fri 9:20 PM a That I com: × 1 8 HW 120. adults, 315 as Latinos, 323 as blacks, 254 identified themselves as Asians, and 779 identified themselves as whites. In this survey, 86% of blacks said that their families would welcome a white person into their famililes assume that the underlying population is normally distributed. (In general, you must first prove that assumption Part (a) O X is the proportion of families that approve of interracial dating and mariage, and P is the number of familes that approve of interracial dating and marriage. Xisthe number of tamiles hat approve ofinte racial dating and man age, and Pis the proportion of familes that approve of inemaal dating and marriage. Part (b) Which distribution should you use for this problem? (Round your answers to four decimal places.) 0084 The Student's I-distribution should be used because we do not know the standard deviation. 16

Explanation / Answer

For part (b)

The normal distribution

Mean p = p^ = 0.86

Here n = 323 as there are 323 blaces

so Mean proportion E(p) = p^ = 0.86

Std Deviation of proportion = sqrt (p^ * (1- p^)/N) = sqrt [0.86 * 0.14/323] = 0.0193

(c) Here error bound = (0.8978 - 0.82222)/2 = 0.0378

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