Sodium Contents of Foods The amount of sodium (in milligrams) in one serving for a random sample of three different kinds of foods is listed here. At the 0.005 level of significance, is there sufficient evidence to conclude that a difference in mean sodium amounts exists among condiments, cereals, and desserts? Condiments Cereals Desserts 110 164 250 270 202 300 130 289 360 130 234 300 180 241 160 80 260 208 70 220 171     470 H0: u1=u2=u3=u4 --------- claim or not? H1: At least one mean is different from the others--------claim or not? Find the critical value Compute the test value: F = Reject or do not reject the null hypothesis Summarize: Is there or is there not enough evidence to support claim? Is there or is there not enough evidence to reject the claim?

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 + ...