Question

A doctor claims that the number of births by day of the week is uniformly distributed. To test this claim, you randomly select 700 births from a recent year and record the day of the week on which each takes place. The table shows the results.

Day:	Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
Births:	68(100)	107(100)	117(100)	110(100)	114(100)	109(100)	75(100)

Test the doctor's claim at the significance level a=0.05.

a) What is the assumed proportion of births in each day?(in fractions)

b) State H0 and Ha.

c) What is the degrees of freedom of the test?

d) Calculate the x^2 test statistic.

e) Decide whether to reject the null hypothesis.

g) Interpret the decision in the context of the original claim.

Answer 1

a)

assumed proportion of births in each day =1/7

b)

Ho: births by day of the week is uniformly distributed

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

c)

degree of freedom =categories-1=

6

d)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
Sun	1/7	68.0	100.00		10.240
Mon	1/7	107.0	100.00		0.490
Tue	1/7	117.0	100.00		2.890
Wed	1/7	110.0	100.00		1.000
Thu	1/7	114.0	100.00		1.960
Fri	1/7	109.0	100.00		0.810
Sat	1/7	75.0	100.00		6.250
total	1.000	700	700		23.6400
test statistic X2 =		23.64

e)

for 0.05 level and 6 df :crtiical value X2 =				12.592
Decision rule: reject Ho if value of test statistic X2>12.592

since test statistic falls in rejection region we reject null hypothesis

g)

we have sufficient evidence to conclude that  births by day of the week is not uniformly distributed