A popular urban legend is that more babies than usual are born during certain phases of the lunar cycle, especially near the full moon. A paper classified a random sample of 1,009 births at a large hospital in a certain country according to lunar phase. In each lunar cycle (27.32 days), the moon moves 360 relative to the earth. To determine lunar phase, the researchers divided the 3600 in one lunar cycle into 12 phases of 300. The sample data are summarized in the following frequency table. Lunar Phase Number of (degrees) Births 0-30 91 31-60 31 61-90 76 91-120 89 121-150 90 151-180 76 181-210 94 211-240 79 241-270 76 271-300 79 301-330 93 331-360 85 LA USE SALT The researchers concluded that the frequency of births is not related to lunar cycle. Carry out a chi-square 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. Let P1' P2' P3' PA' Ps' Pg' Py' Pg' Per Pior Pair and p12 be the proportions of births during the twelve lunar phases. State the appropriate null and alternative hypotheses. OH: P1 = P2 = P3 = PA = P5 = P6 = P7 = P8 = Pg = P10 = P11 = P12 = 12 Ha: Ho is not true. O Ho: P1 = P2 = P3 = PA = P5 = P6 = P7 = Pa = Pg = P10 = P11 = P12 = 1,009 H : H, is not true. O H: P, = P2 = P3 = PA = Ps = P6 = P7 = P8 = Pg = P10 = P11 = P12 = 0.5 H. : H is not true. O HO: P1 = P2 = P3 = PA = P5 = P6 = P7 = Pa = Pg = P10 = P11 = P12 = 0.05 H. : H is not true. OH: P, = P2 = P3 = PA = Ps = P6 = P, = Pa = Pg = P10 = P11 = P12 = 84 He: Ho is not true. Calculate the test statistic. (Round your answer to two decimal places.) x 2 = Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value =