Let x be a random variable that represents micrograms of lead per liter of water(ug/l).An industrial plant discharges water into a creek. The Environmental Protection Agency has studied the discharged water and found x to have a normal distribution, with o=0.7 ug/L The industrial Plant says that the population mean value of x is u = 2.0 ug/L.However a random sample of n= 10 water samples showed that x = 2.56ug/L.Does this indicate that the lead-concentration population mean is higher that the industrial plant claims ? Use a= 1% Find a 95% confidence interval for u using the sample data and the EPA value for o. How large a sample should be taken to be 95% confident that the sample mean /X is within a margin of error E= 0.2 ug/L of the population mean ?

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 + ...