Question

If there is no seasonal effect on human​ births, we would expect equal numbers of children to be born in each season​ (winter, spring,​ summer, and​ fall). A student takes a census of her statistics class and finds that of the 120 students in the​ class, 24 were born in​ winter, 38 in​ spring, 34 in​ summer, and 24 in fall. She wonders if the excess in the spring is an indication that births are not uniform throughout the year.

​a) What is the expected number of births in each season if there is no​ "seasonal effect" on​ births?

​b) Compute the

chi squared

statistic.

​c) How many degrees of freedom does the

chi squared

statistic​ have?

.

Answer 1

a)

expected number =total/4 =120/4 =30

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
Winter	0.250	24.000	30.00	-1.10	1.200
Spring	0.250	38.000	30.00	1.46	2.133
summer	0.250	34.000	30.00	0.73	0.533
fall	0.250	24.000	30.00	-1.10	1.200
total	1.000	120	120		5.067

chi squared statistic =5.067

c)

degree of freedom =categories-1=

3