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