Arsenic occurs naturally in some ground water and can be toxic. A mean arsenic level of μ=9 parts per billion (ppb) is considered safe for agricultural use. A well in San Bernardino County is used to water strawberry crops. This well is tested on a regular basis for arsenic. A random sample of 42 tests gave a sample mean of 8.5 ppb arsenic, with a sample standard deviation of 2.1 ppb. Does this information indicate that the mean level of arsenic in this well is less than μ=9ppb? Use α=0.005 What is the level of significance? State the null and alternate hypotheses.

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 + ...