The weight of a carton of a dozen eggs produced by a certain breed of hens is supposed to be normally distributed with a mean of 780 grams. A quality manager randomly checks thirty-five cartons of eggs (n = 35) to see whether the mean weight differs from 780 grams. She finds x̄ = 796.   1. Assume that the p-value was calculated to be 0.03. Interpret this p-value in context. a.The probability of getting a sample mean more extreme than the one we observed (796g) is equal to 0.03 assuming the population mean is not 780g. b.The probability of rejecting the null hypothesis is 0.03. c. The probability that our sample mean of 796g is equal to the true population mean is 0.03. d. The probability of getting a sample mean as extreme or more extreme than 796g is equal to 0.03 assuming the population mean is 780g.

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 + ...