Question: A sampling distribution. Exercise concerns the mean of the random numbers generated by a computer program. The mean is supposed to be 0.5 because the numbers are supposed to be spread at random between 0 and 1. We asked the software to generate samples of 100 random numbers repeatedly. Here are the sample means for 50 samples of size 100:
The sampling distribution of x is the distribution of the means from all possible samples. We actually have the means from 50 samples. Make a histogram of these 50 observations. Does the distribution appear to be roughly Normal, as the central limit theorem says will happen for large enough samples?
Exercise: Testing a random number generator. Our statistical software has a "random number generator" that is supposed to produce numbers scattered at random 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 = 0.536 and s = 0.312. Give a 90% confidence interval for the mean of all numbers produced by the software.