When wildlife biologists study small animals, the animals are trapped and then a

Question

When wildlife biologists study small animals, the animals are trapped and then anesthetized to prevent discomfort to the animal and safety from disease transmission to the biologist. A study of the effect of the anesthetic, Isoflurane, on Allegheny woodrats (Neotoma magister) resulted in the heartbeat data presented below. The biologists were interested in comparing the effects of Isoflurane in two different seasons, winter and summer.

Pulse (heartbeats/min)

An initial analysis of the data revealed that it was reasonable to assume the distributions of heartbeats for both seasons are approximately normal.

a) Construct a 95% confidence interval for the difference in heartbeat rate for winter and summer. It was also judged to be reasonable to regard these samples as representative of the Allegheny woodrat population.

b) Do the data indicate that the heartbeat rates differ? Justify your answer statistically using your response in part (a).

Group Summer Winter Sample size 24 13 Mean 347.5 360.0 Standard deviation 80.83 133.04

Explanation / Answer

a)here let winter is 1 and summer is 2.

from above

as both are from same population we assume that variance are equal

hence degree of freedom =n1+n2-2 =13+24-2=35

hence pooled std deviation Sp =(((n1-1)s12+(n2-1)s22)/(n1+n2-2))1/2 =101.793

hence std error =(Sp(1/n1 +1/n2)1/2 =35.054

at 95% CI, and 35 degree of freedom t =2.03

hence confidence interval=(X1-X2) +/- t*std error =(-58.664 ; 83.664)

b) as our confidence interval contains 0 as probable value for difference we does not have sufficient evidence to conclude that heart rates differ,

S1 133.040 S2 80.830 n1 13 n2 24 X1 360.000 X2 347.500

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