Mean-and-Variance-of-the-Sample-Means (2).pptx

Can be used in teaching Statistics and Probability

1. Finding the Mean and Variance of the Sampling Distribution of the Sample Means

2. Activity 1 ACTIVITY 1: Consider a population consisting of 1, 2, 3, 4, and 5. Suppose samples of size 2 are drawn from this population. Describe the sampling distribution of the sample means.

3. Activity 1 Compute the mean of the population. Compute the variance of the population. = -  

4. Activity 1 3. Determine the number of possible samples of size n = 2. 4. List all possible samples and their corresponding means. 5. Construct the sampling distribution of the sample means.

5. Activity 1 Compute the mean of the sampling distribution of the sample means. Compute the variance of the sampling distribution of the sample means.

6. Activity 1 Sample Means from a Finite Population ACTIVITY 2 : Consider a population consisting of 1, 2, 3, 4, and 5. Suppose samples of size 3 are drawn from this population. Describe the sampling distribution of the sample means.

7. Activity 1 ACTIVITY 1 ACTIVITY 2 Population (N = 5) Sampling Distribution of the Sample Means (n = 2) Population (N = 5) Sampling Distribution of the Sample Means (n = 3) Mean 3.00 3.00 3.00 3.00 Variance 2.00 0.75 2.00 0.33 Standard Deviation 1.41 0.87 1.41 0.57

8. Activity 1 Properties of the Sampling Distribution of Sample Means Mean of the sampling distribution of the sample means is equal to the population mean.

9. Activity 1 Variance: = . ; for finite population Variance: = ; for infinite population  

10. Activity 1 Finite population – consists of a finite or fixed number of elements, measurements, or observations. Infinite Population – contains, hypothetically at least, infinitely elements.

11. Activity 1 Finite population correction factor Standard error of the mean = standard deviation of the sampling distribution of the sample means  

12. Activity 1 Standard error of the mean = measures the degree of accuracy of the sample mean as an estimate of the population mean.

13. Activity 1 The Central Limit Theorem If random samples of size n are drawn from a population, then as n becomes larger, the sampling distribution of the mean approaches the normal distribution, regardless of the shape of the population distribution.

14. Activity 1 Describing the Sampling Distribution of the Sample Means from an Infinite Population

15. Activity 1 1. A population has a mean of 60 and a standard deviation of 5. A random sample of 16 measurements is drawn from this population. Describe the sampling distribution of the sample means by computing its mean and standard deviation.

16. Activity 1 2. The heights of male college students are normally distributed with a mean of 68 inches and a standard deviation of 3 inches. If 80 samples consisting of 25 students each are drawn from the population, what would be the expected mean and SD of the resulting sampling distribution of means?