Question

A survey by the Pew Research Center asked a random sample of 2142 U.S. adults and a random sample of 1055 college presidents how they would "rate the job the higher education system is doing in providing value for the money spent by students and their families." Their choices were: Excellent, Good, Only Fair, or Poor. 5% the U.S. adults and 17% of the college presidents provided a rating of "Excellent." Calculate the standard error of the difference in sample proportions (for adults minus presidents) based on this data. Round your answer to 4 decimal places

Answer 1

Answer: 0.0125

Step-by-step explanation:

Given :  A survey by the Pew Research Center asked a random sample of 2142 U.S. adults and a random sample of 1055 college presidents how they would "rate the job the higher education system is doing in providing value for the money.

5% the U.S. adults and 17% of the college presidents provided a rating of "Excellent."

i.e. $n_1=2142,\ n_2=1055$

$p_1=0.05$ , $p_2=0.17$

The standard error of the difference in sample proportions  :-

$\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}$

$=\sqrt{\dfrac{0.05(1-0.05)}{2142}+\dfrac{0.17(1-0.17)}{1055}}\\\\=0.0124867775151\approx0.0125$

Hence, the standard error of the difference in sample proportion = 0.0125