Sampling and sampling distributions

Statistics and Probability Grade XI

1. What is a sample? Why study it?

2. SAMPLING - the method of gathering information about a population by taking a representative of the population called sample

3. Can the data gathered from the sample be used to make inferences about the population?

4. Statistically speaking, yes.

5. However, every sample has a different statistic. And this statistic is also considered a random variable because the data vary from one sample to another.

6. SAMPLING AND SAMPLING DISTRIBUTIONS SAMPLING SAMPLING DISTRIBUTION OF STATISTIC STATISTICS PARAMETERS NORMAL DISTRIBUTION t DISTRIBUTION SIMPLE RANDOM SAMPLING SYSTEMATIC SAMPLING STRATIFIED SAMPLING CLUSTER SAMPLING is used to formulate is done to generate to approximate may follow is done using the methods

7. SAMPLING METHODS

8. Simple Random Sampling Systematic Random Sampling Stratified Sampling Cluster Sampling

9. SIMPLE RANDOM SAMPLING

10. - involves selecting a sample size n from a population of size N so that all elements of the population have equal chances of being part of the sample.

11. lotteries tables of random numbers automatic random number generator

12. SYSTEMATIC RANDOM SAMPLING

13. - involves using a random start to determine the first element of the sample and the selection of the rest of the sample is done systematically, i.e., every kth interval, where k = N/n.

14. STRATIFIED SAMPLING

15. - involves dividing the population into groups called STRATA according to some chosen classification category such as age, gender, geographic location, and so on. Subsample from each stratum are selected by simple random sampling.

16. CLUSTER SAMPLING

17. - the elements of the population are divided into groups called CLUSTERS. Clusters are naturally occurring like barangays, cities, or municipalities. Samples are obtained from each cluster by SRS.

18. SLOVIN’S FORMULA - Used to calculate the sample size n given the population size N and a margin of error e.

19. Slovin's formula is used when nothing about the behavior of a population is known at all.

20. EXERCISES Determine the sampling method to be used in each scenario.

21. EXERCISES Determine the sampling method to be used in each scenario.

22. 1. From a list containing the names of 500 members of an alumni association, a sample size of 50 is obtained by including every 10 th person in the list in the sample.

23. 2. The students in a given school are classified according to grade level. Twenty students from each group will be randomly chosen to participate in a study involving students’ study habits.

24. 3. All the students who belong to ten chosen sections in a certain school will participate in a study designed to improve students’ critical thinking skills.

25. 4. A researcher is interested in studying the effects of diet on the attention span of third-grade students in a large city. There are 1,500 third-graders attending the elementary schools in the city. The researcher selects 150 of these third-graders, 30 each in five different schools , as a sample for study.

26. 5. An administrator in a large urban high school is interested in student opinions on a new counseling program in the district. There are six high schools and some 14,000 students in the district. From a master list of all students enrolled in the district schools, the administrator selects a sample of 1,400 students (350 from each of the four grades, 9–12) to whom he plans to mail a questionnaire asking their opinion of the program.

27. 6. The principal of an elementary school wants to investigate the effectiveness of a new U.S. history textbook used by some of the teachers in the district. Out of a total of 22 teachers who are using the text, she selects a sample of 6. She plans to compare the achievement of the students in these teachers’ classes with those of another 6 teachers who are not using the text.

28. ACTIVITY

29. Using the members of your class as the population, use AGE as the quantitative variable of interest and obtain a sample size of 10 using the four sampling techniques. Calculate the sample mean age (statistics) of your data and compare it with the population mean (parameter). Do this by triads in a one whole piece of paper.

30. QUESTION: Which of the four sampling techniques produced statistics which is closest to the population parameters? farthest? What does this imply?