Final answer:
When estimating confidence intervals, people typically provide estimates that are too narrow. The size of a confidence interval depends on the point estimate, margin of error, confidence level, and standard error of the mean. Adjustments in the confidence level, such as going from 99 percent to 90 percent, result in narrower intervals. When people estimate confidence intervals, they typically provide estimates that are too narrow (c).
Step-by-step explanation:
A confidence intervalis a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter. The width of the confidence interval is determined by the point estimate, margin of error, confidence level, and standard error of the mean. People often underestimate variability in the sample, which leads to narrower confidence intervals than what is statistically appropriate.
A confidence interval with a 99 percent confidence level will be wider than a 95 percent one because it aims to include more of the distribution (99 percent vs. 95 percent). When constructing confidence intervals, insufficient sample sizes or the misuse of the sample standard deviation as an estimate for the population standard deviation can lead to inaccuracies, especially with small sample sizes. Therefore, statisticians have developed rules of thumb for sample size that need to be considered when creating confidence intervals.
If we have a survey about the proportion of American adults who download music weekly, the confidence interval would change if the confidence level decreased from 99 percent to 90 percent; the interval would become narrower because we would be less confident that our interval contains the true population parameter.