Statistics: 10% Rule

Objectives

• Students will recognize that when samples are taken from a finite population without replacement the sampling distribution of sample means has a smaller standard deviation than that for samples of equal size taken with replacement.
• Students will understand that calculating the standard deviation of the sampling distribution of sample means applies reasonably well for samples taken without replacement provided the sample size n is no larger than 10% of the population size N.

About the Lesson

This lesson involves investigating the differences between the standard deviations of sampling distributions of means for samples taken from finite populations with and without replacement.
As a result, students will:

• Confirm that the "textbook formula" for the standard deviation of the sampling distribution of sample means is exactly correct when samples are selected with replacement.
• Observe that the standard deviation for sampling distributions of sample means is consistently smaller than that given by the textbook formula when samples are selected without replacement.
• Conclude that the textbook formula for the standard deviation of the sampling distribution of sample means is reasonably correct for samples taken without replacement provided samples are no larger than ten percent of the population size.
• Confirm that the factor corrects the discrepancy between the actual standard deviation of the sampling distribution of sample means for samples without replacement and the value given by the formula for samples with replacement.