Confidence Intervals and Point Estimation | STA 100, Study notes of Statistics

Download Confidence Intervals and Point Estimation | STA 100 and more Study notes Statistics in PDF only on Docsity! STA 100 Lecture 10 Confidence Intervals I. Introduction A Practical Problem: We are interested in studying the effect of high cholesterol level of fathers in the cardiovascular fitness of their offspring. In particular, we would like to know if the cholesterol level of their 12-14 year children is higher than normal. What are the steps for conducting this study? How can we obtain a confidence interval for the average cholesterol level? II. Point Estimation a. A point estimator of a parameter is a statistic used to estimate that parameter. Examples: b. Properties of a “good” estimator are: 1. Unbiasedness: An estimator of a parameter is unbiased if its expected value is equal to the parameter. Example: 2. Minimum Variance: 3. Consistency: III. Interval Estimation a. Confidence Interval: A random interval which covers the true value of a parameter with a given probability. b. Confidence Interval for μ when σ is known: Recall the Central Limit Theorem, which states that for large n (n ≥ 30), the sample mean is approximately normal with mean μ and standard deviation σ/√n. 95% confidence interval: 90% confidence interval: 2