help please this one has been bugging me Number of Leaves pe

help, please this one has been bugging me

Number of Leaves per Whorl in Ceratophyllum demersum. After spending a year with Karl Pearson in London, biometrician Raymond Pearl published his work on mathematical and statistical modeling of growth of an aquatic plant, Ceratophyllum demersum (Pearl. 1907).1 Among several interesting data sets, Pearl gives the table of frequencies of numbers of leaves per whorl. Are the observed frequencies consistent with binomial Bin (12, p) distribution?

Solution

The test is done using excel

p value is very small. Hence the binomil dsitribution is not a good fit to the data.

leaves(x)	whorls(f)	fx	expected frequeinces	approximated expected frequncies
5	10	50	47.87651	50
6	165	990	143.8435	146
7	258	1806	317.5151	320
8	495	3960	511.0523	512
9	733	6597	584.9299	587
10	617	6170	451.9038	453
11	48	528	211.5944	213
12	2	24	45.40921	47
	2328	20125	2314.125	2328
	mean=20125/2328=8.6447
	np=8.6447
	12p=8.6447
	p=8.6447/12=0.7203