Consider the experiment designed to compare four treatment means - u1, u2, u3, and u4- using sample sizes of size n1, n2, n3, and n4 and sample variances s 1 2, s 2 2 , s 2 3 and s 2 4.  a) suppose the sample sizez are the same: n1= n2= n3= n4. show that s2w is the average of the four sample variances: s2w= (s2 1 + s 2 2 + s 2 3 + s 2 4)/4.  b) Does this hold if the sample sizes are not equal ? if not, why not just use the average

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.