Each of the following examples could be addressed with a goodness-of-fit test. From the information given, how many categories and how many degrees of freedom would each test have? Explain your answers.

a. A die is rolled 50 times to test whether it is fair—whether it has a  chance of coming up on each of its six different sides.

b. A food-protection agency counts the number of insect heads found per 100-gram batch of wheat flour. The researchers have 500 batches, and they want to know whether the frequency of insect heads in batches follows a Poisson distribution. The 500 batches included at least 5 batches having 0, 1, 2, 3, or 4 insect heads. No batches had more than four heads.

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