Based on a random sample of 84 students taken at Williams College, the table shows how many had their birthday in the first, second, third, or fourth quarter of the year. Is there evidence that the probabilities of having a birthday in a given quarter are not equal?

a. Formulate the null and alternative hypotheses.
b. Find the expected values and compute the chi-squared statistic, either by hand or using software.
c. The test will be based on how many degrees of freedom?
d. Find the P-value and write a conclusion in context.

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Birthday Jan-Mar Jul-Sep Oct-Dec Apr-Jun 21 п 13 19 31 84