stat 200 week 5 questions illowsky 130

Q. An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the 1709 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.
a. we are interested in finding the 95% confidence interval for the percent of all black adults who would welcome a white person into their families. Define the random variables X and P’, in words
– X is number of black people who would welcome a white person into their families. P’ is the proportion of people in a sample of black people who would welcome a white person

b. which distribution should you use for this problem? Explain your choice.
-N (0.86, square root of (0.86)(0.14)/323). because it is a proportion problem.

c. Construct a 95% confidence interval.
n=323 (did not use 1709 because they are interested in all black adults)
P’= 0.86 q’=1-0.86= 0.14 CL= 95% a=1-0.95= 0.005 0.005/2 = 0.025
area to the left is o.975 look up z table, value is 1.96
EBP = (1.96)(square root of (0.86)(0.14)/323)= 1.96 x 0.019 =0.037
p’+- 0.037 0.86+ 0.037= 0.897 0.86 – 0.037 = 0.823
so CI (0.823, 0.897)