Random Number Generators
The purpose of this exercise is to determine whether a random number generator really produces a random sequence of observations. Using your graphing calculator or favorite statistical software:
a. Generate 100 observations from a standard normal distribution.
b. Classify each observation as either above or below the mean (and median) 0.
c. Conduct a runs test using the normal approximation to determine whether there is any evidence to suggest that the sequence of observations is not random with respect to the mean. Use a = 0.05.
Do this 100 times. How many times did you reject the null hypothesis H0: The sequence is random? Draw a conclusion about the sequence of observations produced by your random number generator.