A popular urban legend is that more babies than usual are born during certain phases of the lunar cycle, especially near the full moon. The paper “The Effect of the Gravitation of the Moon on Frequency of Births” (Environmental Health Insights [2010]: 65–69) classified a random sample of 1007 births at a large hospital in Japan according to lunar phase. In each lunar cycle (27.32 days), the moon moves 360º relative to the earth. To determine lunar phase, the researchers divided the 360º in one lunar cycle into 12 phases of 30º. The sample data are summarized in the accompanying frequency table.

Lunar Phase (degrees) .................... Number of Births
0–30 ............................................................ 90
31–60 .......................................................... 81
61–90 .......................................................... 76
91–120 ........................................................ 87
121–150 ...................................................... 90
151–180 ...................................................... 76
181–210 ...................................................... 94
211–240 ...................................................... 79

241–270 ...................................................... 76
271–300 ...................................................... 80
301–330 ...................................................... 93
331–360 ...................................................... 85

The researchers concluded that the frequency of births is not related to lunar cycle. Carry out a chisquare goodness-of-fit test to determine if the data are consistent with the researchers’ claim. Use a significance level of 0.05 for your test.