oologists studying two populations of tigers conducted a two-sample tt-test for the difference in means to investigate whether the tigers in population X weigh more, on average, than the tigers in population Y. Two independent random samples were taken, and the difference between the sample means was calculated. All conditions for inference were met, and the test produced a p-value of 0.02. Which of the following is a correct interpretation of the p-value? A)The probability that the mean weight for tigers in population X is greater than that for population Y is 0.02.   B).The probability that the mean weight for tigers in population X is equal to that for population Y is 0.02.   C)Assuming that the mean weights for populations X and Y are equal, the probability of observing a difference equal to the sample difference is 0.02.   D)Assuming that the mean weights for populations X and Y are equal, the probability of observing a difference as great or greater than the sample difference is 0.02.   E)Assuming that the mean weight for population X is greater than the mean weight for population Y, the probability of observing a difference as great as or greater than the sample difference is 0.02.

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 + ...