Question: A fast-talking salesman offers you a “random digits” smartphone app that comes with a “guarantee” of randomness. You don’t trust him, so you insist on testing the app by generating a sample of 100 digits. Here are the resulting frequencies of the ten digits 0 through 9 in your sample of size 100:

Digit 0 1 2 3 4

Frequency 12 11 11 4 9

Digit 5 6 7 8 9

Frequency 9 12 10 10 12

With the salesman getting more nervous by the minute, you then conduct a goodness-of-fit test of the null hypothesis that the app’s digits are indeed random (that is, that the probability of seeing any of the ten digits 0 through 9 in a single observation is equal to 1/10 or 0.10) against the alternative that they are not random. Which one of the following analyses of the conditions for performing this test is correct? Justify your answer and also say why the others are NOT correct.

A. Since the data do not come from a simple random sample of possible digits produced by the app, the conditions for performing the test have not been met.

B. Since all the observed counts are not greater than 5, the conditions for performing the test have not been met.

C. All conditions for performing this test have been satisfied.