1. Sampling error occurs because sample means are not equal to the population mean and differ from each other. 2. The distribution of sample means follows a normal distribution if drawn from a normal population, and approximates a normal distribution if drawn from a non-normal population as the sample size increases. 3. A confidence interval for the population mean or probability can be constructed given the sample size, mean or probability, and standard deviation. The confidence level indicates the probability the true population parameter falls within the interval.

7. (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.

8. 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)

15. 3.2.2 The probability density and critical values of t distribution

17. 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 ,

22. 3.4 Confidence Interval for the Difference between Two Population Means unknown. Two samples with The confidence interval for ?

26. Comparing to the confidence interval of

27. 3.5.2 Confidence intervals for two population probabilities

28. Comparing to the confidence interval of