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 1,001 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 360° in one lunar cycle into 12 phases of 30°. The sample data are summarized in the following frequency table. Lunar Phase (degrees) 0-30 31-60 61-90 91-120 121-150 151-180 181-210 211-240 241-270 271-300 301-330 331-360 Number of Births 88 81 76 84 90 76 93 79 76 80 93 85 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 P4 P5 P6 P7 P8 P9 P10 P11 and P12 be the proportions of births during the twelve lunar phases. State the appropriate null and alternative hypotheses. Ho: P₁ = P₂ = P3 P4 P5 = P6 P7 P8 = P9 = P10 P11 = P12 = 1,001 H: Ho is not true. = 0.05 Ho: P₁ = P₂ = P3 = P4 = Ps= P6 = P7 = Ps= P9 = P10 = P11 = P12 = H₂: Ho is not true. Ho: P₁ P₂ P3 P4 P5 = P6 = P7 P8 = P9 = P10 P11 = = P12 = 12 H: H is not true. Ho: P₁ = P₂ = P3 = P4 = Ps= P6 = P7 = Ps= P9 = P10 = P11 = P12 = 83 H: Ho is not true. Ho: P₁ = P₂ = P3 = P4 = P₁ = P6 = P7 = Ps= Pg = P10 = P11 = P12 = 0.5 H₂: Ho is not true. Calculate the test statistic. (Round your answer to two decimal places.) x² = Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = 0 X