Question: A patron wishes to test the randomness of the device used to generate the first digit in the Daily Number Game®. The generator is a box with ten ping-pong balls numbered from zero to nine, which allegedly produces, as the first digit, each of the ten possible numbers with equal probability.

The patron observes that in the last sixteen hundred (1600) games the number one was the first digit 175 times.

(a) Formulate the null and alternative hypotheses about a box model.

(b) Compute z and the chance P.

(c) Can we conclude that this so-called random process results in too many ones, or should we attribute any discrepancy to chance variation?