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