In your work for a national health organization, you are aware that for prior studies of the amount of sodium in a certain brand of cereal is 205 milligrams.  Based upon your sample of 25 servings you find a mean sodium content of 218 milligrams, with a standard deviation of 15 milligrams. You want to test the hypothesis that the mean amount of sodium in this brand of cereal differs from the stated mean of 205 milligrams.  For an α = .02 significance level, determine the Critical Value(s) that separate(s) the region of retention from the region(s) of rejection.

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 + ...