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 824 Americans and 12268 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, 432 of Americans and 7629 of Europeans thought the application was risky.

Give a 98% confidence interval for the percent difference (±0.1) between Europe (call them group 1) and the United States:

Answer 1

The 98% confidence interval = (-0.14, -0.056)

Explanations:

From the calculations done in the file attached to this solution

Proportions of Americans that considered the application risky = 0.524

Proportions of Americans that did not considerthe application risky = 0.476

Proportions of Europeans that considered the application risky = 0.622

Proportions of Europeans that did not consider the application risky = 0.377

Standard error of the sample proportion using the formula written in the attached file = 0.018

The 98% confidence interval is also calculated as in the attached file and gotten as (-0.14, -0.056)