Suppose the weights (in pounds) of eight rowers on each of the Cambridge and Oxford crew teams are given below. Assume that these men represent appropriate random samples from the population of members of these crew teams over all time. Test the hypothesis that the mean weights of the populations of rowers on the Cambridge and Oxford crew teams over all time are equal versus the alternative that they are not equal. (Let population 1 be the Cambridge team and population 2 be the Oxford team. Use ? = 0.05.) Cambridge: 188.0, 182.5, 195.0, 185.5, 214.5, 204.0, 186.5, 178.0 Oxford: 186.5, 185.0, 204.5, 185.0, 195.0, 202.0, 173.5, 182.5   State the null and alternative hypotheses (in pounds). (Use Cambridge − Oxford. Enter != for ≠ as needed.) H0:     Ha:     Find the test statistic. (Round your answer to two decimal places.)   Use technology to find the p-value. (Round your answer to four decimal places.) p-value = Make a reasonable conclusion based on the p-value. Reject H0. There is insufficient evidence to conclude that the mean weights of rowers on the Cambridge and Oxford teams over all time are different.Reject H0. There is sufficient evidence to conclude that the mean weights of rowers on the Cambridge and Oxford teams over all time are different.     Fail to reject H0. There is insufficient evidence to conclude that the mean weights of rowers on the Cambridge and Oxford teams over all time are different.Fail to reject H0. There is sufficient evidence to conclude that the mean weights of rowers on the Cambridge and Oxford teams over all time are different.

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 + ...