1. SAMPLING DISTRIBUTIONS Let’s do a little review :

2. SAMPLING DISTRIBUTIONS Let’s do a little review : A statistic is a numerical descriptive measure of a sample.

3. SAMPLING DISTRIBUTIONS Let’s do a little review : A statistic is a numerical descriptive measure of a sample. A parameter is a numerical descriptive measure of a population.

4. SAMPLING DISTRIBUTIONS Let’s do a little review : A statistic is a numerical descriptive measure of a sample. A parameter is a numerical descriptive measure of a population. From a statistical point of view, a population can be thought of as a complete set of measurements ( counts ), either existing or conceptual. But it is sometimes impossible to get the entire population as our data set.

5. SAMPLING DISTRIBUTIONS Let’s do a little review : A statistic is a numerical descriptive measure of a sample. A parameter is a numerical descriptive measure of a population. From a statistical point of view, a population can be thought of as a complete set of measurements ( counts ), either existing or conceptual. But it is sometimes impossible to get the entire population as our data set. Imagine if we wanted to find the average height of 15 year old males in the United States? We might take years to get all the data which makes it impractical.

6. SAMPLING DISTRIBUTIONS Let’s do a little review : A statistic is a numerical descriptive measure of a sample. A parameter is a numerical descriptive measure of a population. From a statistical point of view, a population can be thought of as a complete set of measurements ( counts ), either existing or conceptual. But it is sometimes impossible to get the entire population as our data set. Imagine if we wanted to find the average height of 15 year old males in the United States? We might take years to get all the data which makes it impractical. So we SAMPLE the population by maybe only measuring the height of fifty random 15 – year old males in each state.

7. SAMPLING DISTRIBUTIONS Let’s do a little review : A statistic is a numerical descriptive measure of a sample. A parameter is a numerical descriptive measure of a population. From a statistical point of view, a population can be thought of as a complete set of measurements ( counts ), either existing or conceptual. But it is sometimes impossible to get the entire population as our data set. Imagine if we wanted to find the average height of 15 year old males in the United States? We might take years to get all the data which makes it impractical. So we SAMPLE the population by maybe only measuring the height of fifty random 15 – year old males in each state. We can then make inferences on the entire population based on the sample data or our population parameter.

8. SAMPLING DISTRIBUTIONS We have different types of inferences :

9. SAMPLING DISTRIBUTIONS We have different types of inferences : 1. Estimation – we can estimate the value of a population parameter

10. SAMPLING DISTRIBUTIONS We have different types of inferences : 1. Estimation – we can estimate the value of a population parameter 2. Testing – we can formulate a decision about the value of a population parameter

11. SAMPLING DISTRIBUTIONS We have different types of inferences : 1. Estimation – we can estimate the value of a population parameter 2. Testing – we can formulate a decision about the value of a population parameter 3. Regression – we can make predictions or forecasts about the value of a statistical variable

12. SAMPLING DISTRIBUTIONS We have different types of inferences : 1. Estimation – we can estimate the value of a population parameter 2. Testing – we can formulate a decision about the value of a population parameter 3. Regression – we can make predictions or forecasts about the value of a statistical variable We have worked with frequency tables, relative frequencies, and histograms to help understand sampling distributions.

13. SAMPLING DISTRIBUTIONS We have different types of inferences : 1. Estimation – we can estimate the value of a population parameter 2. Testing – we can formulate a decision about the value of a population parameter 3. Regression – we can make predictions or forecasts about the value of a statistical variable We have worked with frequency tables, relative frequencies, and histograms to help understand sampling distributions. We have also understood what a normal distribution looks like and how we can calculate probabilities of data items occurring or not occurring.

14. SAMPLING DISTRIBUTIONS A SAMPLING DISTRIBUTION is a probability distribution of a sample statistic based on all possible simple random samples of the same size from the same population.

15. SAMPLING DISTRIBUTIONS A SAMPLING DISTRIBUTION is a probability distribution of a sample statistic based on all possible simple random samples of the same size from the same population. Here is an example : Becky has a project for her biometrics class where she has to track the measurements of trout taken from a lake where only children under 12 years old can fish. The kids can keep 5 trout per day and the trout must be 6 inches or longer to keep. Hundreds of children fished the lake last summer so Becky has a lot of data. To make things easier, she decides to choose 100 children at random and list their lengths of each trout kept.

16. SAMPLING DISTRIBUTIONS A SAMPLING DISTRIBUTION is a probability distribution of a sample statistic based on all possible simple random samples of the same size from the same population. Here is an example : Becky has a project for her biometrics class where she has to track the measurements of trout taken from a lake where only children under 12 years old can fish. The kids can keep 5 trout per day and the trout must be 6 inches or longer to keep. Hundreds of children fished the lake last summer so Becky has a lot of data. To make things easier, she decides to choose 100 children at random and list their lengths of each trout kept. Becky can find the mean and standard deviation of the sample she took but what does that really tell her ?

17. SAMPLING DISTRIBUTIONS

19. Class Limits ClassLowerUpper 18.398.7610.01 28.779.1450.05 39.159.52100.10 49.539.90190.19 59.9110.28270.27 610.2910.66180.18 710.6711.04120.12 811.0511.4250.05 911.4311.8030.03 The frequency represents how many children had a mean within the class limits. The relative frequency represents the theoretical probability of a child having a mean within the class limit.

20. SAMPLING DISTRIBUTIONS Class Limits ClassLowerUpper 18.398.7610.01 28.779.1450.05 39.159.52100.10 49.539.90190.19 59.9110.28270.27 610.2910.66180.18 710.6711.04120.12 811.0511.4250.05 911.4311.8030.03 The frequency represents how many children had a mean within the class limits. The relative frequency represents the theoretical probability of a child having a mean within the class limit. You can see the data is pretty close to a normal curve. In fact, if we made a histogram of the data, it is somewhat bell shaped.

21. SAMPLING DISTRIBUTIONS Class Limits ClassLowerUpper 18.398.7610.01 28.779.1450.05 39.159.52100.10 49.539.90190.19 59.9110.28270.27 610.2910.66180.18 710.6711.04120.12 811.0511.4250.05 911.4311.8030.03 The frequency represents how many children had a mean within the class limits. The relative frequency represents the theoretical probability of a child having a mean within the class limit. You can see the data is pretty close to a normal curve. In fact, if we made a histogram of the data, it is somewhat bell shaped. So we have sampling distribution because : a) We have a probability distribution

22. SAMPLING DISTRIBUTIONS Class Limits ClassLowerUpper 18.398.7610.01 28.779.1450.05 39.159.52100.10 49.539.90190.19 59.9110.28270.27 610.2910.66180.18 710.6711.04120.12 811.0511.4250.05 911.4311.8030.03

23. SAMPLING DISTRIBUTIONS Class Limits ClassLowerUpper 18.398.7610.01 28.779.1450.05 39.159.52100.10 49.539.90190.19 59.9110.28270.27 610.2910.66180.18 710.6711.04120.12 811.0511.4250.05 911.4311.8030.03

24. SAMPLING DISTRIBUTIONS So a SAMPLING DISTRIBUTION is : 1. A probability distribution

25. SAMPLING DISTRIBUTIONS

26. 3. Based on all possible samples of the same size

27. SAMPLING DISTRIBUTIONS 3.Based on all possible samples of the same size We will use sampling distributions to make statistical inferences