In a study of media usage versus education level (American Demographics, Vol. 17, No. 6), media usage versus household income also was considered. The media usage indices for the various media and income levels follow.   Media Income Level CableNetwork Prime-TimeTV Radio Newspaper Magazine Less than $20,000 78 112 89 80 91 $20,000-$39,999 97 105 100 97 100 $40,000-$74,999 113 92 106 111 105 $75,000 or more 121 94 107 121 105 Source: From American Demographics, Vol. 17, No. 6. Reprinted with permission, copyright 1995 American Demographics, Ithaca, NY. Minitab Printout for Media/Income Data Analysis of Variance for Index Source DF SS MS F P Income  3 1078 359 2.77 0.088 Media  4  15   4 0.03 0.998 Error 12 1558 130     Total 19 2651   (b) Assume there is no interaction between the factors. Use two-way ANOVA and the Minitab printout to determine if there is a difference in population mean index based on income. Use α = 0.05. F =  P-value =  (c) Determine if there is a difference in population mean index based on media. Use α = 0.05. F =  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 + ...