 For the impatient researcher, on the other hand, the sample space is much smaller. Apart from the sample consisting of six successes, all samples consist of a series of successes ending with a failure, differing only in the length of the series. Yet the probabilities over the two samples of length six are the same as for the diligent researcher. As before, the sample of six successes is again included in the region of rejection. Similarly, the sequence of five successes followed by one failure also has a probability of \(1/64\) under the null hypothesis, against a probability of \(3^5 / 4^{6}\) according to the alternative. The difference is that lowering the likelihood ratio to include this sample in the region of rejection leads to the inclusion of this sample only. And if we include it in the region of rejection, the probability of false rejection becomes \(1/32\) and hence does not exceed 5%. Consequently, on the basis of these data the laid-back researcher can reject the null hypothesis that the lady is merely guessing.