Question

The health center at a college is trying to estimate what proportion of students are experiencing depression or anxiety. The health center will use a confidence level of 95% and a margin of error of 5%. Prior research shows that the prevalence of mental illness in college students is about 15%.

Determine the sample size needed for the study.

Answer 1

The sample size needed for the study to estimate the proportion of college students experiencing depression or anxiety with a 95% confidence level and a margin of error of 5% is approximately 196 students.

Step-by-step explanation:

To estimate the proportion of college students experiencing depression or anxiety with a 95% confidence level and a margin of error of 5%, we need to calculate the sample size needed for the study. The standard formula for determining the sample size for a proportion is:

n = (Z² × p × (1 - p)) / E²

Where n is the sample size, Z is the Z-value associated with the desired level of confidence (1.96 for 95%), p is the estimated proportion of the attribute present in the population (0.15, or 15%), and E is the margin of error (0.05 or 5%).

Substituting the values:

n = (1.96² × 0.15 × 0.85) / 0.05²

n = 196

Approximately 196 students should be surveyed to achieve the desired confidence level and margin of error. It's worth mentioning that this calculation assumes a simple random sample and a large enough population that the sample size doesn't exceed 5% of the total population, which is generally true for college campuses.