# Learn by Doing – Proportions (Step 2) Understanding the Test Statistic

Published: October 22nd, 2013

Category: Activity 1: Learn By Doing

Consider the population of part-time college students. Suppose that 60% of this population is female.

Here is the sampling distribution for the proportion of females in random samples of n students. The standard deviation is approximately 0.10. Lines indicate a distance of 1 and 2 standard deviations above and below the mean.

http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/LBD_12017_prop2.swf

Here is the sampling distribution for the proportion of supporters in random samples of 25 adults. The standard deviation is approximately 0.10.

http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/LBD_12018_prop2.swf

If we increase the sample size to 100, the standard deviation decreases to approximately 0.05, as shown.

http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/LBD_12019_prop2.swf

This document is linked from Proportions (Step 2).