A biology student measured the ear lengths of an SRS of 10 Mountain cottontail rabbits, and an SRS of 10 Holland lop rabbits. The ear lengths for the two samples are listed in the two tables attached (see attached image).   (a) Calculate a 95% confidence interval for the difference in mean ear lengths between Mountain cottontail rabbits and Holland lop rabbits. Make sure to define which is “µ1” and which is “µ2.” (You can complete the calculations either by hand or using R, but remember to show all your work.) (b) Do Holland lop rabbits have longer ears on average than Mountain cottontail rabbits? Carry out a test of significance to answer this question. Show your work at each step. Don’t forget to state the hypotheses at the start (making sure to define all parameters), and to include a conclusion in terms of the original problem. (You can complete the calculations either by hand or using R, but remember to show all your work.

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 + ...