1. Sampling error refers to the sample means not being equal to the population mean and differing from each other. 2. The distribution of sample means follows certain patterns. If drawn from a normal population, the sample mean follows a normal distribution. If from a non-normal population, the distribution approximates normal as sample size increases. 3. Confidence intervals provide a range that is likely to include the true population parameter. Formulas are given for calculating confidence intervals for a population mean, single or two population probabilities, and the difference between two population means or probabilities. Sample size considerations are also discussed.

8. (3) The distribution of sample means follows certain rule that more in center, less in two ends and symmetry around the center. (4) The range of variation for the sample mean is much narrower than that of the initial variable.

9. If the random samples with n individuals are drawn from a normal distribution , then the sample mean follows a normal distribution (3.1) , then the sample mean follows a normal distribution (3.1)

16. 3.2.2 The probability density and critical values of t distribution

18. 3.3 The Confidence Interval for Population Mean of Normal Distribution Therefore, 95% of the sample means meet the inequality (but not all) For any sample, if we claim is located in such an interval, then in theory, we might be right about 95 times out of 100 times. and are unknown A sample is drawn, and ,

23. 3.4 Confidence Interval for the Difference between Two Population Means unknown. Two samples with The confidence interval for ?

27. Comparing to the confidence interval of

28. 3.5.2 Confidence intervals for two population probabilities

29. Comparing to the confidence interval of