Final answer:
A confidence interval is a statistical tool used to estimate the range within which a population parameter is likely to lie based on sample data. To construct it, you collect and calculate sample data, find the Z-score or t-score for your confidence level, and then determine the margin of error for the interval.
Step-by-step explanation:
A confidence interval is a range of values, derived from sample data, that is likely to contain the population parameter. In general terms, if someone has not taken statistics, we could explain that a confidence interval provides a range within which we expect a certain population characteristic, like the average height, to fall, with a given level of certainty or probability.
When constructing a confidence interval for a particular study, we aim to estimate the population parameter, such as the mean or proportion, based on our sample data. For example, if we were investigating the average number of hours students study per week, our confidence interval would provide a range that we believe, with a certain level of confidence, includes the true average.
To create a confidence interval, we first need to collect data, like surveying students on where they were born. We then calculate the sample mean or proportion, find the appropriate Z-score or t-score for our desired confidence level, and then use the standard error to calculate the range around our sample estimate. The formula for a confidence interval is the point estimate plus or minus the margin of error, which is the Z-score or t-score multiplied by the standard error.
It's a common misunderstanding that a 90 percent confidence interval includes 90 percent of the data values; however, it means that if we were to take many samples and construct a confidence interval from each, approximately 90 percent of these intervals would contain the true population mean.
Interpreting confidence intervals requires understanding that they are random variables - they vary from sample to sample - while the population parameter is fixed. Statistical education often includes learning about different distributions, such as the Student's-t distribution, which is used when the sample size is small or the population standard deviation is unknown.