Many people believe that unusual behavior is more likely to occur during a full moon. In fact, they believe that twice as many events happen during the full moon as during the other phases. As a test for empirical evidence to support this belief, suppose that you categorized the visits of new clients to a community health unit over a one-year period by lunar phases and found the following distribution of visits:

Full Moon: 82

New Moon 50

First quarter 40

Third quarter 48

Do new visits vary with the phase of the moon?

Do the appropriate statistical test and write a statement of results.