Why is the chi-square test typically a onetail test with the critical region in the right tail?

a. What kind of value would result if the observed frequencies and the expected frequencies were very close in value? Explain how you would interpret this situation.

b. Suppose you had to roll a die 60 times as an experiment to test the fairness of the die as discussed in the example on pages 622–624; but instead of rolling the die yourself, you paid your little brother $1 to roll it 60 times and keep a tally of the numbers. He agreed to perform this deed for you and ran off to his room with the die, returning in a few minutes with his resulting frequencies. He demanded his $1.

You, of course, pay him before he hands over his results, which are as follows: 10, 10, 10, 10, 10, and 10. The observed results are exactly what you had “expected,” right? Explain your reactions. What value of 2 will result? What do you think happened? What do you demand of your little brother and why? What possible role might the left tail have in the hypothesis test?

c. Why is the left tail not typically of concern?