Question

In an experiment on colour inheritance in a particular flower, of 1135 self-fertilized plants, 270 plants had blue flowers, 300 plants had yellow, and565 had red. Theory predicts the flowers should be 25% blue, 25% yellow, and 50% red. Do the observed data support the theory? If you were to do a goodness of fit test on this data to test the hypothesis that the theory is correct, state to one place of decimal the expected frequency for the yellow cell?

Answer 1

Null hypothesis:Ho: the sample proportion follows the proportion stated by theory

Alternate hypothesis: Ha: the sample proportion does not follows the proportion stated by theory

degree of freedom =categories-1=	2
for 0.05 level and 2 df :crtiical value X2 =		5.991
Decision rule: reject Ho if value of test statistic X2>5.991

applying chi square goodness of fit test:

expected value for yellow =np=1135*0.25 =283.8

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
blue	0.2500	270.0	283.75	-0.82	0.6663
yellow	0.2500	300.0	283.75	0.96	0.9306
red	0.5000	565.0	567.50	-0.10	0.0110
total	1.000	1135	1135		1.6079
test statistic X2 =	1.608

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that the sample proportion does not follows the proportion