Using Low Budget Classroom Exercises to Teach Sampling Techniques

1. Using Low Budget Classroom Exercises to Teach Sampling Techniques By Richard Summers, PhD Reinhardt College Eastern Regional Competency Based Educational Consortium

2. Students Relate Better to Data That Relate to Them • Confidence intervals are more relevant, if the data compare the class to the entire student body • In class activities can suggest student projects • In class activities emphasize the relevance and applicability of statistics

3. Hypothesis Test for a Proportion • Have available the percent male/female enrollment for the college • Count the number of male and female students in the class • Obtain the confidence level at which there is a significant difference between the population and sample proportions • Discuss whether or not the class represents a good sample of the overall student body

4. The Central Limit Theorem (Idea Due to Judith M. Tanur, SUNY) • Have students list their birth month and the birth months of their two closest relatives • Plot all of the above data on a dot plot

5. Central Limit Theorem (continued) • Ask students to find the mean of the three birth months they listed, rounding to the nearest integer • Make a dot plot of the above averages – the data will usually be more symmetrically distributed

6. Random Sampling • Provide a list of classes taught in your school together with class enrollment and mean class enrollment • Use a random number generator to make random choices from the list and note the class size for each choice • Take the mean of the class sizes recorded above

7. Random Sampling(Continued) • Start with a sample of 5 classes and take the mean class size • Add 5 more classes and take the mean of the resulting sample of 10 class sizes • Continue to increase the sample size to emphasize that the sample mean tend to the population mean as the sample size becomes larger

8. Systematic Sampling • Ask every third student as they are seated in the classroom to give their birth month • Take the mean of the above results and compare with the population mean • Do the same by taking every second student

9. Stratified Sampling • Divide the class into freshmen, sophomores, juniors and seniors • Ask 3 students from each group how many hours they are taking • Compare the means for each group

10. Cluster Sampling • Divide the students into groups according to which row they occupy in the classroom • Take 3 students from each row • Take the mean birth month for the sample

11. Χ2 Test for Goodness of Fit • Have at hand a listing of number of majors by school • Have the students state their major school • Tally the results by school • Make a nominal frequency distribution • Use a Χ2 Test to check whether the sample from the class is representative of the college

12. Χ2 Test for Goodness of Fit (Continued) • Discuss any reasons for differences between the class sample and the one for the college • Try the sample again by using data restricted to majors requiring the course