When generating random digits as in Exercise 1, we can test the generated digits for goodness-of-fit with the distribution in which all of the digits are equally likely. What does an exceptionally large value of the X² test statistic suggest about the goodness-of-fit? What does an exceptionally small value of the X² test statistic (such as 0.002) suggest about the goodness-of-fit?

Exercise 1

A New York Times CBS News Poll typically involves the selection of random digits to be used for telephone numbers. The New York Times states that “within each (telephone) exchange, random digits were added to form a complete telephone number, thus permitting access to listed and unlisted numbers.” When such digits are randomly generated, what is the distribution of those digits? Given such randomly generated digits, what is a test for “goodness-of-fit”?