Chapter 9.2, Problem 4Q

Among a number of beliefs concerning the so-called lunar effect is that more children are born during the full moon. The table below gives the average number of births per day during the full moon (lunar fraction $\ge 0.95$) versus the average number during a period of lunar fraction $\le 0.75$. The table shows the opposite effect. The average is smaller during the full moon. But is this a significant difference? Test the equality of means at the 0.05 level of significance. Assume the variances are equal.

Number of Live Births
Full Moon	$3\text{/}4$ Moon or Smaller
$n=109$	$m=494$
$\bar{x}=10732$	$\bar{y}=10970$
$s_X=2017$	$s_Y=1897$