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Cluster sampling examples. Example 1: Assume that a study with relatively large square fixed area plots of 50 m x 50 m had been carried out, on which all tree positions were mapped. Because the individual plots were relatively large, there were only resources available to measure \(n=10\) sample plots.
The example on tea drinkers explained above requires this test. In that example, p0 = 0.5. Notice that in this particular example, proportion refers to the proportion of tea drinkers. z test for difference of proportions is used to test the hypothesis that two populations have the same proportion.