Question

If there is no seasonal effect on human​ births, one 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, 26 were born in​ winter, 36 in​ spring, 32 in​ summer, and 26 in fall. She wonders if the excess in the spring is an indication that births are not uniform throughout the year. Complete parts​ a) through​ c) below.

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

One should expect __ births in​ winter,__ in​ spring, __ in​ summer, and __in fall.

​(Type whole​ numbers.)

b) complete the X^2 statistic to 2 decimals as needed

c) how many degrees of freedom does the X^2 stat have?

Answer 1

a)

One should expect 30 births in​ winter,_30_ in​ spring, _30 in​ summer, and 30_in fall.

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	26	30.00	-0.73	0.533
spring	0.250	36	30.00	1.10	1.200
summer	0.250	32	30.00	0.37	0.133
fall	0.250	26	30.00	-0.73	0.533
total	1.000	120	120		2.400

chi square test statistic X² =2.400

c)

degree of freedom =categories-1=

3