Question

Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds. Over time, the lengths of the flowers and the form of the hummingbirds' beaks have evolved to match each other. Here are data on the lengths in millimeters of three varieties of these flowers on the island of Dominica. data190.dat Do a complete analysis that includes description of the data and a significance test to compare the mean lengths of the flowers for the three species. (Round your answers for x to four decimal places, s to three decimal places, and s_(x^^\_) to three decimal places. Round your test statistic to two decimal places. Round your P-value to three decimal places.) flower type n x^^\_ s s_(x^^\_) H. bihai H. caribaea red H. caribaea yellow F = P =

Answer 1

To test :

H₀ : The mean length of the flowers of the three species are same .

vs.

H₁ :  At least one mean is different

Test statistic :

We reject the null hypothesis or H₀ if the observed value of , where ,

Flower type	n		s
H.bihai	16	48.1631	1.316	0.329
H.caribaea red	23	40.1852	2.303	0.480
H. caribaea yellow	15	35.9073	0.874	0.226

The ANOVA table is given below :

ANOVA

Source	DF	SS	MS	F	p-value
Factor	2	1218.2	609.118	202.63	0
Error	51	153.3	3.006
Total	53	1371.5

The value of the test statistic : F = 202.63

Since , , hence we reject the null hypothesis or H₀ .

Thus there is significant evidence to suggest that atleast one mean length of the flowers is different .