Americans eat about 1.85 billion pounds of potato chips, or about 6.6 pounds per person annually. A study was performed with the group of 32 high school children on the annual potato chip consumption. The mean annual chip consumption among these children was found to be 8.8 pounds with standard deviation 3.5 pounds. a) If the distribution is assumed to be normal, then test the hypothesis that the group of 32 children have annual potato chip consumption different from that in the general population. b) Compute a 95% CI for the true mean annual potato chip consumption in this group. c) What is the p-value for the test?

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 + ...