Point Estimate vs. Interval Estimate

Point Estimate: A point estimate is a single value used to estimate a population parameter. It’s like taking a “best guess” based on sample data.

• Example: Suppose we want to estimate the average height of all adults in a country. We take a random sample of 100 adults, measure their heights, and calculate the sample mean. This sample mean is a point estimate of the population mean height.

Interval Estimate: An interval estimate provides a range of values within which we believe the population parameter lies with a certain level of confidence.

• Example: Using the same example as above, we can construct a 95% confidence interval for the population mean height. This interval would be a range of values, such as (65 inches, 70 inches), and we would be 95% confident that the true population mean height lies within this range.

Interpreting the 95% Confidence Interval

Interpretation: We are 95% confident that the true population mean lies between 56.56 and 62.39.

Meaning of “95% Confidence”: This means that if we were to repeat the sampling process many times and construct 95% confidence intervals for each sample, approximately 95% of those intervals would contain the true population mean.

Effect of Sample Size on Confidence Interval

Increasing the sample size will decrease the length of the confidence interval.

This is because a larger sample size leads to a more precise estimate of the population parameter. As the sample size increases, the standard error of the estimate decreases, resulting in a narrower confidence interval.