Question

The following table lists some of animals that have some of the longest lifespans on earth. Does incubation or gestation time affect an animals average lifespan? Some animals have lifespans that average well over 100 years. Is there a correlation between an animal's gestation/incubation period and their average lifespan in years? A. Draw the scatterplot for the variables b. Describe the relationship, if any, shown by the scatterplot.c. Calculate r, the correlation coefficient. How does the correlation coefficient compare to the relationship you saw in the scatterplot?

Animal:                                             Avg. Lifespan(in years)                   Incubation/Gestation(in Months)

Nile Croc                                                 100                                                        3

Aldabra Giant Tortoise                             152                                                        8

Lake Sturgeon                                           152                                                    0.25

Galapagos Tortoise                                    177                                                   4.7

Bowhead White                                          211                                                    13.5

Answer 1

a)

The data provided is :

Animal	Avg LifeSpan(years)	Incubation(months)
Nile Croc	100	3
Aldabra Giant Tortoise	152	8
Lake Sturgeon	152	0.25
Galapagos Tortoise	177	4.7
Bowhead White	211	13.5

b)

There seems to a positive linear relationship between the variables.

c)

The provided data are shown in the table below

X	Y
100	3
152	8
152	0.25
177	4.7
211	13.5

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	100	3	300	10000	9
	152	8	1216	23104	64
	152	0.25	38	23104	0.0625
	177	4.7	831.9	31329	22.09
	211	13.5	2848.5	44521	182.25
Sum =	792	29.45	5234.4	132058	277.4025

The correlation coefficient r is computed using the following expression:

Therefore, based on this information, the sample correlation coefficient is computed as follows

The correlation coefficient is in line with the relationship we saw in the scatterplot.

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