Deer mice (Peromyscus maniculatus) are small rodents native of North America. Their adult body lengths (excluding tail) are known to vary approximately Normally, with mean μ = 86 mm and standard deviation σ = 8 mm. Deer mice are found in diverse habitats and exhibit different adaptations to their environment. A random sample of 14 deer mice in a rich forest habitat gives an average body length of  = 91.1 mm. Assume that the standard deviation σ of all deer mice in this area is also 8 mm. What is the standard deviation of the mean length . (Report in mm and round to 3 decimals) What critical value do you need to use in order to compute a 95% confidence interval for the mean μ Give a 95% confidence interval for the mean body length of all deer mice in the forest habitat. Give a 90% confidence interval for the mean body length of all deer mice in the forest habitat.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...