Question

A doctor claims that the number of births by day of the week is uniformly distributed. To test the claim, you randomly select births from a recent year and record the day of the week the birth takes place. Use a 1% significance to test the claim.
Round to the fourth as needed.

Day	Sun	Mon	Tues	Wed	Thurs	Fri	Sat
Frequency	56	36	31	42	36	48	52

a) Type out the null and alternative hypothesis

b) State you test statistic

c) State your p-value

d) State your decision rule

e) Type out your conclusion

Answer 1

a)

null hypothesis: Ho: number of births by day of the week is uniformly distributed

Alternate hypothesis: Ha: number of births by day of the week is not uniformly distributed

b)

Applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Sun	1/7	56.000	43.00	1.98	3.930
Mon	1/7	36.000	43.00	-1.07	1.140
Tue	1/7	31.000	43.00	-1.83	3.349
Wed	1/7	42.000	43.00	-0.15	0.023
Thu	1/7	36.000	43.00	-1.07	1.140
Fri	1/7	48.000	43.00	0.76	0.581
Sat	1/7	52.000	43.00	1.37	1.884
total	1.000	301	301		12.047

test statisitc X² =12.047

c)

p value =0.0609

d)

Decision rule: reject HO if p value <0.01 or tst statistic X² <16.812

e)

as test statistic is not in rejection region ; we can not conclude that number of births by day of the week is not uniformly distributed