random sample of 47 filtered cigarettes is obtained and the tar content of each cigarette is measured. The sample has a mean of 19.4 mg and a standard deviation of 3.18 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered cigarettes is less than 21.1 mg, which is the mean for unfiltered cigarettes.  State the final conclusion regarding the claim.  ___________   the HO since the p-value is    _______the significance level α. There is   ________ evidence to support the claim that the mean tar content of filtered cigarettes is less than 21.1 mg, which is the mean for unfiltered

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 + ...