Question

Europeans have been more skeptical than Americans about the use of genetic engineering to improve foods. A sample survey gathered responses from random samples of 855 Americans and 12362 Europeans. (The European sample was larger because Europe is divided into many nations.) Subjects were asked to consider the following issue:

Using modern biotechnology in the production of foods, for example to make them higher in protein, keep longer, or change in taste.

They were asked if they considered this "risky for society." In all, 430 of Americans and 7638 of Europeans thought the application was risky.

Give a 99% confidence interval for the percent difference (±0.1) between Europe (call them group 1) and the United States:   ± %.

Answer 1

Here, , n1 = 12362 , n2 = 855
p1cap = 0.6179 , p2cap = 0.5029

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.6179 * (1-0.6179)/12362 + 0.5029*(1-0.5029)/855)
SE = 0.0176

For 0.99 CI, z-value = 2.58

CI = (p1cap - p2cap +/- ME

= (0.6179 - 0.5029) +/- 2.58 * 0.0176
= 0.115 +/- 0.0454

= 11.5% +/- 4.54%