Listed below are the lead concentrations in muμ​g/g measured in different traditional medicines. Use a 0.010.01 significance level to test the claim that the mean lead concentration for all such medicines is less than 1717 muμ​g/g. Assume that the lead concentrations in traditional medicines are normally distributed.   1010      13.513.5      16.516.5      19.519.5      2121      13.513.5      3.53.5      22.522.5      1313      3.53.5    What are the null and alternative​ hypotheses?     A. Upper H 0H0​: muμequals=1717 muμ​g/g Upper H 1H1​: muμless than<1717 muμ​g/g   B. Upper H 0H0​: muμequals=1717 muμ​g/g Upper H 1H1​: muμgreater than>1717 muμ​g/g   C. Upper H 0H0​: muμequals=1717 muμ​g/g Upper H 1H1​: muμnot equals≠1717 muμ​g/g   D. Upper H 0H0​: muμgreater than>1717 muμ​g/g Upper H 1H1​: muμless than<1717 muμ​g/g Determine the test statistic.     ​(Round to two decimal places as​ needed.) Determine the​ P-value.     ​(Round to three decimal places as​ needed.) State the final conclusion that addresses the original claim.       Upper H 0H0. There is     evidence to conclude that the mean lead concentration for all such medicines is     1717 muμ​g/g

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 + ...