At a Midwestern hospital there were a total of 932 births in 20 consecutive week

Question

At a Midwestern hospital there were a total of 932 births in 20 consecutive weeks. Of those births, 216 occurred on weekends (Saturday and Sunday) and 716 occurred on weekdays (Monday, Tuesday, Wednesday, Thursday, Friday). The goal is to determine if more births occur on the weekends than would happen by chance (by chance is 2/7).

(a) State the null hypothesis.

(b) State the alternative hypothesis.

(c) Calculate the test-statistic.

(d) Is your sample data consistent with your alternative?

(e) Estimate the p-value.

(f) Interpret your p-value in terms of the problem.

(g) Do we reject, or fail to reject the null?

(h) State your conclusion in terms of the problem.

Explanation / Answer

a)null hypothesis: Ho: birth is independent of day of week

b)alternate hypothesis: Ha: birth depends on day of week

c)

test stat chi square =13.29

d) yes as expected frequency >5 in each cell

e)p value for above test stat at 1 degree of freedom =0.0003

f) p value is minimum probabilty to accept the null hypothesis

g) we reject null hypothesis

h) we conclude that more births occur on the weekends than would happen by chance

observed Expected Chi square AR P O E=total*p =(O-E)^2/E weekend 2/7 216 266.2857 9.50 weekdays 5/7 716 665.7143 3.80 932 932 13.29

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