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Powerball is a multistate lottery in which players try to

Powerball is a multistate lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. Between January 18, 2012, and June 26, 2013, a total of 755 balls numbered 1 through 59 were drawn. Following are the observed frequencies.

Perform a test of the null hypothesis that each of the numbers is equally likely to come up. Use the a = 0.05 level.

In a hypothetical study, four hospitals were compared with regard to the outcome of a particular type of surgery. For each patient at each hospital, the outcome was classified as Substantial improvement, Some improvement, or No improvement. The results are presented in the following contingency table.

Perform a test of the null hypothesis that each of the numbers is equally likely to come up. Use the a = 0.05 level.

In a hypothetical study, four hospitals were compared with regard to the outcome of a particular type of surgery. For each patient at each hospital, the outcome was classified as Substantial improvement, Some improvement, or No improvement. The results are presented in the following contingency table.

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