Question

An article regarding interracial dating and marriage recently appeared in a newspaper. Of the 1708 randomly selected adults, 307 identified themselves as Latinos, 322 identified themselves as blacks, 255 identified themselves as Asians, and 777 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.)

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

Welcome a white person (_____,_______)

Welcome a Latino   (_____,_______)

Welcome a black person (_____,_______)

B. Even though the three point estimates are different, do any of the confidence intervals overlap? Which? (Select all that apply.)

Yes, the intervals for whites and Latinos overlap.

Yes, the intervals for Latinos and blacks overlap.

Yes, the intervals for whites and blacks overlap.

No confidence intervals overlap.

Yes, all three intervals overlap.

Answer 1

given that

the number of Asian =n=255

the proportion of Asians who welcome whites =

the proportion of Asians who welcomes latino=

the proportion of Asians who welcomes black persons=

since for the normality we need to check that if

now

now 95% confidence interval for three Asian responses

1) who welcomes white

so interval (0.7400,0.8400)

2)

who welcome Latino

hence interval (0.6543,0.7657)

3)

who welcome black

Hence interval (0.6019,0.7181)

as we see clearly that intervals for whites and Latino overlap while Latino and black overlap hence

Yes, the intervals for whites and Latinos overlap.

Yes, the intervals for Latinos and blacks overlap.