Learn Statistics

  I. Introduction to Confidence Intervals: A confidence interval is a range of values that is likely to include the true parameter of interest. In the context of estimating the mean, it provides a range within which we are reasonably confident the true population mean lies. Confidence intervals are useful because they convey both point estimates and a measure of uncertainty. II. Basics of Confidence Intervals for the Mean: Formula for Confidence Interval: � ˉ ± � ( � � ) x ˉ ± t ( n ​ s ​ ) � ˉ x ˉ is the sample mean. � t is the critical t-value from the t-distribution. � s is the sample standard deviation. � n is the sample size. III. The t-Distribution: The t-distribution is used when the sample size is small or when the population standard deviation is unknown. It is similar to the normal distribution but has fatter tails, accommodating the additional uncertainty associated with small sample sizes. IV. Calculating the Critical t-Value: The critical t-value is determined by...