Deer mice. Deer mice ( Peromyscusmaniculatus ) are small rodents native to North

Question

Deer mice. Deer mice (Peromyscusmaniculatus) are small rodents native to North America. Their body lengths excluding tails is known to vary approximatelyNormally with mean µ = 86 mm and standarddeviation = 8 mm. Deer mice arefound in diverse habitats and exhibit different adaptations totheir environment. A random sample of 14 deer mice in a richforest habitat gives an average body length of `x= 91.1 mm. Assume that the standard deviation of all deer mice in this area is 8 mm.Show any work.

a.       What is the standarddeviation of the mean length `x ?

b.      What critical value do you need toin order to compute a 95% confidence interval for the meanµ?

c.       Calculate a 95% confidenceinterval for the mean body length of all deer mice in the foresthabitat.

d.      State explicitly what thisconfidence level means.

Explanation / Answer

a.   a) standard deviation of the mean length`x = standard error(e) = /n =8/14 = 2.14

b.   b) critical value you need to in order tocompute a 95% confidence interval for the mean µ isthe value of z which can be found from the z table andwhich is equal to 1.96.

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