wo subspecies of dark-eyed juncos were studied by D. Cristol et al. One of the subspecies migrates each year, and the other does not. Several characteristics of 14 birds of each subspecies were measured, one of which was wing length (in millimeters). The summaries of two samples are as follows: migratory subspecies has a sample mean wing length of 82.1 millimeters with standard deviation of 1.5 millimeters; non-migratory subspecies had a sample mean wing length of 84.92 millimeters with standard deviation of 1.69 millimeters. Assume that wing lengths in populations of subspecies are normally distributed. Conduct a hypothesis test to determine if there is a significant difference between mean wing lengths of the two subspecies. a. The appropriate hypotheses are b. Degree of freedom, test statistic and p-value are c. At the significance level calculated in part (b), we conclude that: i. The difference between mean wing lengths of the two subspecies is statistically significant ii. The difference between mean wing lengths of the two subspecies is not statistically significant

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 + ...