Final answer:
To construct a confidence interval, we use data from a random sample to estimate the interval in which a population parameter lies. The sample mean and standard deviation are used as point estimates for the population mean and standard deviation, and the interval constructed provides a range with a specified level of confidence that the population parameter will fall within.
Step-by-step explanation:
The correct answer to the question, 'To construct a confidence interval, what is used?' is D) Random sample is used to construct the interval of the population parameter. When constructing a confidence interval, we rely on inferential statistics to make generalizations about an unknown population parameter using data from a random sample. The sample mean (x) and sample standard deviation (s) serve as point estimates for the population mean (μ) and population standard deviation (σ), respectively. The confidence interval provides a range where the true population parameter is expected to lie with a certain level of confidence, for example, 95% confident.
If we have a larger interval, the confidence level increases, meaning we are more certain that the interval contains the population mean. Conversely, a smaller sample size tends to result in greater variability, and thus a larger interval is necessary to maintain the same level of confidence. If multiple confidence intervals are constructed from repeated sampling, we would expect, say 90% of them (for a 90% confidence level) to contain the true population mean.
It's important to construct these using only the sample data, because we typically do not have access to the entire population data. The goal is to estimate the population parameters, not to describe the sample itself. This is a fundamental concept in inferential statistics and forms the basis for many statistical analyses in research and decision making.