Testing a random number generator. Statistical software has a “random number generator” that is supposed to produce numbers uniformly distributed between 0 to 1. If this is true, the numbers generated come from a population with μ = 0.5.

A command to generate 100 random numbers gives outcomes with mean x = 0.522 and s = 0.316. Because the sample is reasonably large, take the population standard deviation also to be σ = 0.316. Do we have evidence that the mean of all numbers produced by this software is not 0.5?