Question

What conditions are necessary in order to use the z-test to test the difference between two population proportions? Choose the correct answer below O A. Each sample must be randomly selected, dependent, and n1P1. n191, n2P2, and n292 must be at least five ○ B. Each sample must be randomly selected, dependent, and nıp,n1q1-n2p2, and n2q2 must be at most five. O C. Each sample must be randomly selected, independent, and niP1, n11. n2P2. and n2q2 must be at most five. O D. Each sample must be randomly selected, independent, and nip1. nq1. n2P2, and n2q2 must be at least five.

Answer 1

To use the z-test to test the difference between two population proportions, each sample must be randomly selected and independent, and each sample must have at least five successes and five failures.

Step-by-step explanation:

When testing a single population proportion with the z-test, the following conditions are necessary:

1. Each sample must be randomly selected and independent.
2. The number of successes and number of failures in each sample must be at least five.

The z-test can be used to test the difference between two population proportions if these conditions are met.

Answer 2

For a z-test comparing two population proportions, each sample must be random, independent, and both samples must have at least five successes and five failures.

Step-by-step explanation:

To use the z-test for testing the difference between two population proportions, certain conditions need to be met:

• The samples must be randomly selected.
• The samples must be independent of each other.
• Both samples must satisfy the success-failure condition, which means the number of successes (np1 and np2) and the number of failures (nq1 and nq2) in each sample must be at least five.

The correct answer that reflects these conditions is option D: "Each sample must be randomly selected, independent, and n1P1, n1q1, n2P2, and n2q2 must be at least five."