STATISTIC and PROBABILITY Week 7 ppt.ppt
- 2. Statistics and Probability Day 5, PM 2
- 3. Session Objectives At the end of the session, the participants will be able to 1.illustrate random sampling 2.distinguish between parameter and statistic 3.identify sampling distributions of statistics (sample mean) 4.find the mean and variance of the sampling distribution of the sample mean
- 4. 5. define the sampling distribution of the sample mean for the normal population when the variance is (a) known and (b) unknown 6. illustrate the Central Limit Theorem (CLT) 7. define the sampling distribution of the sample mean using the CLT 8. solve problems involving sample distributions of the sample mean
- 5. Activity: “Sample Mo, Rand(a)m ‘Ko” Directions: Charades is a game of pantomimes. Team leader will pick up a category and will act out the word/phrase written on a piece of paper without speaking, while the other members of the team will guess what the phrase/word is. The objective is to guess the phrase as quickly as possible. Correct answer will be rewarded with 1 point.
- 6. Category
- 7. Sampling Distributions Standard Error of the Sampling Distribution of the Sample Proportion Mean of the Sampling Distribution of the Sample Proportion The Central Limit Theorem Variance and Standard Deviation of the Sampling Distribution of the Sample Mean Mean of the Sampling Distribution of the Sample Mean Sampling Distribution of the Sample Proportion Sampling Distribution of the Sample Mean
- 8. Four Types of Random Sampling 1.Simple Random Sampling is a sampling technique in which every element of the population has the same probability of being selected for inclusion in the sample. 2.Systematic Random Sampling is a sampling technique in which every kth element of the population is selected until the desired number of elements in the sample is obtained. The value of k is calculated by dividing the number of elements in the population by the number of elements in the desired sample. The value of k is the sampling interval.
- 9. 3. Stratified Random Sampling is a sampling technique in which the population is first divided into strata and then samples are randomly selected separately from each stratum. 4. Cluster or Area Sampling is a random sampling technique in which the entire population in broken into small groups, or clusters, and then, some of the clusters are randomly selected. The data from the randomly selected clusters are the ones that are analyzed.
- 10. Exercises: Identify the type of sampling technique used by the researcher in each situation: 1.The office clerk gave the researcher a list of 500 Grade 10 students. The researcher selected every 20th name on the list. 2. A researcher selected a sample of n = 120 from a population of 850 by using the Table of Random Numbers. Systematic Random Sampling Simple Random Sampling
- 11. 3. A statistician selected a sample of n = 100 high school students from a private school with 2,500 students. He randomly selected the students from each year level. 4. A researcher randomly selected 5 barangays from 10 barangays in a town. Stratified Random Sampling Cluster Random Sampling
- 13. Sampling Distribution of Sample Means
- 14. Example : Consider the population consisting of the values 2, 3, and 5. List all the possible samples of size 2 that can be drawn from the population with replacement. Then, compute the mean x for each sample. Lastly, find the mean of the sampling distribution of means and the mean of the population.
- 16. Exercises Refer to worksheets and answer part I - II.
- 17. x
- 18. Example: Consider the population consisting of the values (1, 3, 8). a. Find the population mean, variance and standard deviation. b. List all the possible samples of size 2 with replacement. c. Compute the mean of each sample. d. Identify the probability of each sample. e. Compute the mean of the sampling distribution of the means. f. Find the variance of the sampling distribution of means. g. Find the standard deviation of the sampling distribution of means.
- 20. Solution: x
- 21. Exercise Refer to the worksheet and answer part III.
- 23. Sample x (1, 1) 1.0 (1, 3) 2.0 (1, 5) 3.0 (3, 1) 2.0 (3, 3) 3.0 (3, 5) 4.0 (5, 1) 3.0 (5, 3) 4.0 (5, 5) 5.0 Consider the population consisting of the values (1, 3, 5). List all the possible samples of size 2 with replacement. 1 2 3 4 5 6 1/9 3/9 2/9 4/9
- 24. Sample x (1, 3) 2.0 (1, 5) 3.0 (3, 1) 2.0 (3, 5) 4.0 (5, 1) 3.0 (5, 3) 4.0 Consider the population consisting of the values (1, 3, 5). List all the possible samples of size 2 without replacement. 1 2 3 4 5 1/6 3/6 2/6 4/6
- 26. x
- 28. Exercises Refer to the worksheet and answer part IV
- 29. Closure