Are low-fat diets or low-carb diets more effective for weight loss? A sample of 51 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 1.8 kilograms with a sample standard deviation of 4.03 kilograms. A second sample of 54 subjects went on a low-fat diet. Their sample mean weight loss was 3.1 kilograms with a standard deviation of 4.74 kilograms. Can you conclude that the mean weight loss of subjects having low-carb diets is less than the mean weight loss of subjects having low-fat diets? Let μ1 denote the mean weight lost on the low-carb diet and μ2 denote the mean weight lost on the low-fat diet. Use the α=0.01 level and the TI-84 Plus calculator. a)State the appropriate null and alternate hypotheses b)Compute the P-value. Round the answer to four decimal places. c)Determine whether to reject H0. d) There (is/is not) enough evidence to conclude that the mean weight loss of subjects having low-carb diets is less than the mean weight loss of subjects having low-fat diets.

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 + ...