Question

Question Helo If there is no easonal effect on human births, we would expect equal numbers of chndren to be bom in each season winser, spring summer and an Adentes a consus of the and finds that of the 120 students in the class. 28 were born in winter 33 in spring, 31 nummer, and 28 infall She wonder if the excess in the spring is an indication that bith anotunto throughout the year aj What is the expected number of birth in each season there is no seasonal effect on birth? by Compute they statistic c) How many degrees of freedom does the statistie have? al The expected number of birth in each beason there is no 'seasonal effect (Type anveger or a decimal DIY-Round to three decimal places as needed. (Type an integer or a decis

Answer 1

a)The null and alternative hypothesis

H0: The births are uniformly distributed over seasons

Ha : The births are not uniformly distributed over seasons

As under null hypothesis ,it is expected that births are not effected by season , births are uniformly distributed over the seasons

Expected births in each season is given by

season	Ei
winter	30
spring	30
summer	30
fall	30

b) Test statistic

2 -Σ (Οι – Εί)? Ei

where Oi : observed frequency

Ei : expected frequency

The calculation of chi square

season	Oi	Ei	(Oi-Ei)^2/Ei
winter	28	30	0.13333333
spring	33	30	0.3
summer	31	30	0.03333333
fall	28	30	0.13333333
sum			0.600

Thus

0.600

x =

c) degrees of freedom = n-1 = 4-1 3

df = 3

Note : P value = 0.8964 ( using excel function "=CHISQ.DIST.RT(0.6,3)" )

Since P value > 0.05

We fail to reject H0

There is not sufficient evidence to conclude that births are not uniformly distributed over the year .