Question

10. (17 pts) A person wants to determine whether the proportion of children born each day of the week is the same or not in a city; that is, the expected relative frequencies are as follows: Day of Week Relative Frequency Sunday 1/7 Monday 1/7 Tuesday 1/7 Wednesday 1/7 Thursday 1/7 Friday 1/7 Saturday 1/7 The person randomly selected a sample of 500 children and the result is as follows: Day of Week Frequency Sunday 57 Monday 78 Tuesday 74 Wednesday 76 Thursday 71 Friday 81 Saturday 63 At the α = 0.01 level of significance, is there evidence that the proportion of children born each day of the week is the same?

Answer 1

degree of freedom =categories-1=

6

for 0.01 level and 6 degree of freedom :rejection region =

16.812

applying chi square goodness of fit 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	57	71.43	-1.71	2.915
mon	1/7	78	71.43	0.78	0.605
tue	1/7	74	71.43	0.30	0.093
wed	1/7	76	71.43	0.54	0.293
thu	1/7	71	71.43	-0.05	0.003
fri	1/7	81	71.43	1.13	1.283
sat	1/7	63	71.43	-1.00	0.995
total	1.000	500	500		6.184

from above test statistic =6.184

as test statistic is less than critical value we can not reject null hypothesis ; we do not have sufficient evidence at 0.01 level to conclude that proportion of children born each day of the week is different