Question

To construct a confidence interval for the difference of two population proportions, the samples must be independently obtained random samples, both must consist of less than 5% of the population. What other condition(s) must be satisfied?

Option 1: The populations must have the same size
Option 2: The populations must have the same standard deviation
Option 3: The populations must be normally distributed
Option 4: The sample proportions must be greater than 0

Answer 1

To construct a confidence interval for two population proportions, samples must be drawn from normally distributed populations, each sample should have at least five successes and five failures, and populations must be independent of each other.

Step-by-step explanation:

To construct a confidence interval for the difference of two population proportions, aside from the samples needing to be independently obtained random samples and each being less than 5% of the population, certain conditions must be satisfied:

• The samples must be drawn from normally distributed populations.
• Both samples should consist of at least five successes and five failures (np > 5 and nq > 5).
• The populations must be independent of each other.

These conditions ensure the accurate calculation of the confidence interval by satisfying the requirements that allow approximation to a normal distribution. Populations do not necessarily have to be the same size (Option 1) or have the same standard deviation (Option 2). While Option 4 mentions that sample proportions must be greater than 0, the more accurate condition requires the number of successes and failures in each sample to be at least five. This follows the rule for the minimum expected counts in statistical tests involving proportions.