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SUMMARYIn a sampling problem for selecting the better of two binomial populations with a fixed total sample size, two sampling rules are shown to have equal probabilities of correct selection. One of them is the so-called Play-the-Winner sampling rule and the other is the usual Vector-at-a-Time sampling rule. As a corollary it is also shown that for the Play-the-Winner rule the expected number of observations on the poorer treatment, i.e. on the population with smaller p, is never greater than for the Vector-at-a-Time rule.
< 6 < 1. Our goal is to keep down to a mini11D.1m both a) the expected number of observations on the poorer treatment (i.e., treatment 2) and Q) the expected total number of observations. We are mainly concerned with a comparison of the play-the-winner (PW) and vector-at-a-time {VT) sampling rules that are used in Procedures ¾»w and l\rr, respectively, both based on a fixed total sample size N. Under the PW sampling rule, we select one population at random at the outset.
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