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 826 Americans and 12321 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, 445 of Americans and 7818 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

We need to construct the 98% confidence interval for the difference between population proportions p_1 - p_2p1​−p2​. We have been provided with the following information about the sample proportions:

Favorable Cases 1	7818
Sample Size 1	12321
Favorable Cases 2	445
Sample Size 2	826

The sample proportion 1 is computed as follows, based on the sample size N_1 = 12321 and the number of favorable cases X_1 = 7818

The sample proportion 2 is computed as follows, based on the sample size N_2 = 826 and the number of favorable cases X_2 = 445

The critical value for α=0.02 is z_c = 2.326. The corresponding confidence interval is computed as shown below:

CI = (0.054, 0.137)