The Economist collects data each year on the price of a Big Mac in various countries around the world. The price of a Big Mac for a sample of McDonalds restaurants in Europe in May 2009 resulted in the following Big Mac prices (after conversion to U.S. dollars):
3.80 5.89 4.92 3.88 2.65 5.57 6.39 3.24
The mean price of a Big Mac in the U.S. in May 2009 was $3.57. For purposes of this exercise, assume it is reasonable to regard the sample as representative of European McDonalds restaurants. Does the sample provide convincing evidence that the mean May 2009 price of a Big Mac in Europe is greater than the reported U.S. price? Test the relevant hypotheses using α = .05. Assume a normal distribution of the data. x¯x¯=; ss= H0H0: μ=μ= HaHa: μμ     (Put in the correct symbol and value) α=α= P-value =

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 + ...