Final answer:
A random variable is used to refer to an outcome and is defined by the numerical results of a random process. When constructing a confidence interval, one should define the random variable, select an appropriate distribution, construct the interval using sample statistics, sketch the graph, and calculate the error bound. The confidence level chosen affects the width of the interval.
Step-by-step explanation:
Among the given options, random variable would be the term used to refer to an outcome. A random variable is a variable whose possible values are numerical outcomes of a random phenomenon. For example, if X is a random variable representing the number of DVDs a customer rents, the possible values X could take on might be 0, 1, 2, 3, etc., depending on how many DVDs are rented. To construct a confidence interval for a population mean, one typically assumes a certain distribution, calculates the sample mean and standard deviation, determines the error bound, and uses these to estimate the range within which the population mean likely falls with a specified level of confidence.To approach such a problem Define the random variable X in words, outlining what it represents in the context of the question.Choose an appropriate distribution based on the context and sample data. Common distributions include the normal distribution for continuous data or the binomial distribution for discrete data.Construct the confidence interval using the chosen distribution, the sample statistics, and the desired confidence level. The confidence interval provides an estimated range for the population parameter, and the confidence level indicates the degree of certainty (e.g., 90%, 95%, 99%) associated with that interval estimate.Sketch the graph to visualize the confidence interval on a distribution curve.Calculate the error bound, which is the margin of error associated with the interval estimate.The choice of confidence level affects the width of the confidence interval, with higher levels resulting in wider intervals. This is because a higher confidence level requires a greater range to ensure the true population parameter is captured within the interval.