We have just conducted a study comparing cognitive development of low- and normal birthweight babies who have reached 1 year of age. Using a scale we devised, we found that the sample means of the two...

We have just conducted a study comparing cognitive development of low- and normal birthweight babies who have reached 1 year of age. Using a scale we devised, we found that the sample means of the two groups were 25 and 30, respectively, with a pooled standard deviation of 8. Assume that we wish to replicate this experiment with 20 subjects in each group. If we assume that the true means and standard deviations have been estimated exactly, what is the a priori probability that we will find a significant difference in our replication?