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, 23 were born in​ winter, 38 in​ spring, 33 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.

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

​b) Compute the χ2 statistic.

​c) How many degrees of freedom does the χ2 statistic​ have?

Answer 1

a)

If there is no seasonal effect, then the births are uniform throughout the year.

So, expected number of births in each season would be =

b)

Chi squarestatistic value =

where Oi and Ei are observed and expected frequencies.

c)

We know that the degress of freedom for this chi square test would be given by: