1. Sampling Error SAMPLING ERROR-SINGLE MEAN The difference between a value (a statistic) computed from a sample and the corresponding value (a parameter) computed from a population. Where:

2. Sampling Distributions sampling distribution A sampling distribution is a distribution of the possible values of a statistic for a given size sample selected from a population.

3. Sampling Distribution of the Mean THEOREM 6-1 If a population is normally distributed with a mean  and a standard deviation , the sampling distribution of the sample mean based on n observations is also normally distributed with the same mean and a standard deviation of.

4. Sampling Distribution for n=4

5. Histogram of Individual Values

6. Histogram Compared to the Dot Plot of Averages

7. Sampling Distribution of the Mean THEOREM 6-2: THE CENTRAL LIMIT THEREOM For samples of n observations taken from a population with mean  and standard deviation , regardless of the population’s distribution, provided the sample size is sufficiently large, the distribution of the sample mean, will be approximately normal.

8. Sampling Distribution of the Mean THE CENTRAL LIMIT THEREOM (Continued) 4 The mean of the distribution of is equal to the population mean. The standard deviation will equal the population standard deviation divided by the square-root of the sample size. 4 The larger the sample size, the better the approximation to the normal distribution.

9. Simulating the 500 Rolls of n Dice

13. Sampling Distribution of the Mean Z-VALUE FOR SAMPLING DISTRIBUTION OF where:= Sample mean = Population mean = Population standard deviation n = Sample size

14. Example of Calculation z-Value for the Sample Mean (Example 6-5) What is the probability that a sample of 100 automobile insurance claim files will yield an average claim of $4,527.77 or less if the average claim for the population is $4,560 with standard deviation of $600?