At a western hospital there was a total of 932 births in 20 consecutive weeks. Of...

At a western hospital there was a total of 932 births in 20 consecutive weeks. Of these births, 216 occurred on weekends. Based on these data, are birth rates different on weekends and weekdays?

a) Name two statistical methods that could be used to test hypotheses. State the advantages and disadvantages of both.

Expert Solution

If the timing of births is random, then 2/7 of all births should occur on weekends, and 5/7 on weekdays. Do
births deviate from this random timing?
Let pi1 be the probability that a birth occurs on a weekend.
Let pi2 be the probability that a birth occurs on a weekday.
H0: pi1 = 2/7 = 0.286; pi2 = 5/7 = 0.714. The births have random weekend/weekday timing
HA: pi1 not equal to 2/7, pi2 not equal to 5/7 ; The timing of births do not have random weekend/weekday timing.
Use a x2 GOF test.

/E has a X21 dist'n under H0. Critical value is 3.84 with ALPHA = 0.05.
n = 932 births; observed 216 on weekends and 932-216 = 716 on weekdays

PI1* =216/932 = 0.232
PI2*= 716/932 = 0.768 (Note that

PI1* < PI1 and
PI2*> PI2 )
Expected under H0: E1= n *PI1 = (932)(2/7) = 266.3
E2 = n *PI2 = (932)(5/7) = 665.7

Reject H0 since 13.3 > 3.84.
This study provides evidence that fewer births occur on weekends at this hospital than would be predicted by
random timing of the births

orchestra answered 1 year ago

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