Final answer:
The question pertains to constructing a confidence interval for a population proportion in a college-level statistics course, using the sample proportion, Z-score, and ensuring the sample size is adequate for the normal approximation.
Step-by-step explanation:
The subject of the question is clearly Mathematics, specifically, the topic is focused on statistics and involves constructing a confidence interval for a population proportion (p). This is a common question in a college-level statistics course. To construct a confidence interval for p, we would typically use the formula for a confidence interval for a population proportion which is p' ± Z*(√(pq/n)), where p' is the sample proportion, q' is 1 minus the sample proportion, n is the sample size, and Z is the Z-score corresponding to the desired level of confidence.
For instance, if the sample proportion is 0.53, the sample size is 100, and we are looking for a 95% confidence interval, we need to find the Z-score that corresponds to 95% confidence (which is approximately 1.96 for a two-tailed test), calculate q' as 0.47, and use the formula to find the interval. It is important to ensure that the sample size is large enough so that both np' and nq' are greater than five, assuring that the normal approximation is valid.