Have American males (AMs) gotten heavier over the last 20 years? A random sample 77 AMs in 2019 had a mean weight of x = 189.030 pounds. A random sample 93 AMs in 1999 had a mean weight of y = 184.795 pounds. It is recognized that the true standard deviation of 2019 AMs weights is σx = 14.04 pounds while it is recognized that the true standard deviation of 1999 AMs weights is σy = 10.03 pounds. The true (unknown) mean of 2019 AMs weights is μx pounds, while the true (unknown) mean of 1999 AMs weights is μy pounds. Weights are known to be a normally distributed. In summary: Type Sample Size Sample Mean Standard Deviation 2019 Data (X) 77 189.030 14.04 1999 Data (Y) 93 184.795 10.03 d) Calculate the standard deviation of X - Y? . e) If we wish to create an 98% confidence interval for μx-μy then what is the z critical value used? f)Create an 98% confidence interval for μx-μy .

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 + ...