Question

True? When we collect random samples to test the claim that the proportion of female CIA agents stationed in the United States is equal to the proportion of female CIA agents stationed outside the United States, there is a requirement that \(np \ge 30\) and \(nq \ge 30\).

Short answer

It is false that there is a requirement of \(np \ge 30\) and \(nq \ge 30\) to test the claim that the proportion of female CIA agents stationed in the United States is equal to the proportion of female CIA agents stationed outside the United States.

Step-by-step solution

Given information

It is required to test the claim that the proportion of female CIA agents stationed in the United States is equal to the proportion of female CIA agents stationed outside the United States.

Requirement of z-test

To test the given claim, a z-test for the testing the equality of two proportions needs to be conducted.

One of the requirements of the z-test is\(np \ge 5\)and\(nq \ge 5\). That is, the number of successes and the number of failures in each of the two samples should be at least equal to 5.

Here, n stands for the sample size, p stands for the proportion of success, and q stands for the proportion of failures.

Therefore, the given statement that there is a requirement of\(np \ge 30\)and\(nq \ge 30\)totest the claim that theproportion of female CIA agents stationed in the United States is equal to the proportion of female CIA agents stationed outside the United States is false.