The purpose of a study by Ingle and Eastell (A-10) was to examine the bone mineral density (BMD) and ultrasound properties of women with ankle fractures. The investigators recruited 31 postmenopausal women with ankle fractures and 31 healthy postmenopausal women to serve as controls. One of the baseline measurements was the stiffness index of the lunar Achilles. The mean stiffness index for the ankle fracture group was 76.9 with a standard deviation of 12.6. In the control group, the mean was 90.9 with a standard deviation of 12.5. Do these data provide sufficient evidence to allow you to conclude that, in general, the mean stiffness index is higher in healthy postmenopausal women than in postmenopausal women with ankle fractures? Let alpha = .05

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 + ...