Final answer:
The method sample_proportions(sample_size, model_proportions) is used to simulate drawing samples from a population with a known proportion of categories, which is useful for estimating population proportions, testing hypotheses, or simulating surveys.
Step-by-step explanation:
The method sample_proportions(sample_size, model_proportions) is used in statistics to simulate sampling from a population with known proportions. This is particularly relevant when dealing with categorical data where there are two outcomes, often labeled as Success or Failure, Yes or No. For example, it can be used to estimate what proportion of a population will vote for a certain candidate or what proportion has a college-level education.
When invoking this method, sample_size denotes the number of random samples to draw, and model_proportions represents the true proportions of categories in the population. The output is an array of sample proportions that estimates the population proportions. This function can be useful for creating confidence intervals, hypothesis testing, or simulating surveys and experiments.
In the context of confidence intervals, the formula for the sample proportion p' is p' = x/n, where x is the number of successes and n is the sample size. The sample proportion p' serves as a point estimate for the true population proportion. When comparing two sample proportions to test if they reflect a difference in population proportions, a hypothesis test is employed using a pooled proportion for the calculation.