3. The text Introduction to Statistics and Data Analysis by Roxy Peck, Chris Ols

Question

3. The text Introduction to Statistics and Data Analysis by Roxy Peck, Chris Olsen and Jay Devore gives two years worth of data for births and the lunar cycle collected to explore whether more babies than normal are born during a full moon. The data for number of days in each portion of the lunar cycle and number of babies born during each portion of the lunar cycle is given below. Are proportionally more babies born during a full moon than should be expected? Moon Phase New Waxing First Waxing Full Waning Last Waning Moon Crescent Quarter Gibbous Moon Gibbous QuarterCrescent 152 Days 24 152 24 149 24 150 24 Babies Born 7,680 48,442 7,579 47,814 7,711 47,595 7.,733 48,230

Explanation / Answer

H0 : Proportions of babies born on full moon is same as the expected proportion of baby born on full moon. p = p0

Ha : Proportions of babies born on full moon is significantly higher than the expected proportion of baby born on full moon. p > p0

where p0 = full moon days/ total number of days = 24/699 = 0.03433

Here sample proportion of babies born on full moon p^ = Full moon babies/ Total babies born = 7711/222784 = 0.03461

standard error of proportion se0 = sqrt [po (1-p0)/N] = sqrt [0.03461 *0.96579/222784] = 3.8728 x 10-4

Here test statistic

Z = (0.03461 - 0.03433)/ 3.8728 x 10-4 = 0.723

p - value = Pr(Z > 0.723) = 0.7652 > 0.05 so we shalln't reject the null hypothesis and can conclude that Proportions of babies born on full moon is same as the expected proportion of baby born on full moon.

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