A number of years ago, the mean on the verbal section of the GRE was 489 with a standard deviation of 126. The statistics were computed for native speakers of English. Suppose we have an application from a person with a Chinese name who scored 255.
In order to hazard a conclusion about the native language of the individual, we perform a z-score calculation and obtain -1.86. Using a one-tailed test, the probability that this score comes from the native English-speaking population is 0.0314.
How would the test have differed if we had chosen to run a two-tailed test with the same alpha of

Question

A number of years ago, the mean on the verbal section of the GRE was 489 with a standard deviation of 126.  The statistics were computed for native speakers of English.  Suppose we have an application from a person with a Chinese name who scored 255.
 In order to hazard a conclusion about the native language of the individual, we perform a z-score calculation and obtain -1.86.  Using a one-tailed test, the probability that this score comes from the native English-speaking population is 0.0314.
 How would the test have differed if we had chosen to run a two-tailed test with the same alpha of