The difference between a point estimate and an interval estimate
Sample Solution
Point Estimates vs. Interval Estimates
Point Estimate: A single value used to estimate a population parameter.
- Example: Using the sample mean (x̄) as a point estimate for the population mean (μ).
Full Answer Section
Interval Estimate: A range of values used to estimate a population parameter with a certain degree of confidence.
- Example: A 95% confidence interval for the population mean.
Interpreting the Confidence Interval
Interpretation: We are 95% confident that the true population mean lies between 56.56 and 62.39.
Meaning of "95% Confidence": If we were to take many samples 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 at a fixed confidence level.
This is because a larger sample size leads to a smaller standard error, which in turn reduces the margin of error.
A smaller margin of error results in a narrower confidence interval, providing a more precise estimate of the population parameter.