Listed below are the numberss of years that archbishops and monarchs in a certain country lived after their election or coronation. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.01 significance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. All measurements are in years مطمعصصممصممصمطمنط طمعممم صنشمعصملعمملطمعطفعشمفص صمنمطفعلصنلم i Longevities of Archbishops and Monarchs OA. O c. 16 Archbishops 13 18 13 14 1 15 17 9 15 10 13 14 14 14 14 16 17 6 17 12 4 15 15 Monarchs 14 16 Click t 20 13 16 19 15 15 15 16 16 16 ? З ра ren Check Answer Print Done

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 + ...