In a study of media usage versus education level (American Demographics, Vol. 17, No. 6), an index was used to measure media usage, where a measurement of 100 represents the U.S. average. Values above 100 represent above-average media usage. Media Education Level CableNetwork Prime-TimeTV Radio Newspaper Magazine Less than high school 80 112 87 76 85 High school graduate 103 105 100 99 101 Some College 107 94 106 105 107 College graduate 108 90 106 116 108 Source: From American Demographics, Vol. 17, No. 6. Reprinted with permission, copyright 1995 American Demographics, Ithaca, NY. Minitab Printout for Media/Education Data Analysis of Variance for Index Source DF SS MS F P Edu 3 961 320 2.96 0.075 Media 4 5 1 0.01 1.000 Error 12 1299 108 Total 19 2264 b) Assume there is no interaction between the factors. Use two-way ANOVA and the following Minitab printout to determine if there is a difference in population mean index based on education. Use α = 0.05. STEP 2: Find the test statistic and P-value. F = P-value = (c) Determine if there is a difference in population mean index based on media. Use α = 0.05. Find the test statistic and P-value. F = P-value =

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In a study of media usage versus education level (American Demographics, Vol. 17, No. 6), an index was used to measure media usage, where a measurement of 100 represents the U.S. average. Values above 100 represent above-average media usage.

	Media
Education Level	Cable Network	Prime-Time TV	Radio	Newspaper	Magazine
Less than high school	80	112	87	76	85
High school graduate	103	105	100	99	101
Some College	107	94	106	105	107
College graduate	108	90	106	116	108
Source: From American Demographics, Vol. 17, No. 6. Reprinted with permission, copyright 1995 American Demographics, Ithaca, NY.

Minitab Printout for Media/Education Data
Analysis of Variance for Index
Source	DF	SS	MS	F	P
Edu	3	961	320	2.96	0.075
Media	4	5	1	0.01	1.000
Error	12	1299	108
Total	19	2264

b) Assume there is no interaction between the factors. Use two-way ANOVA and the following Minitab printout to determine if there is a difference in population mean index based on education. Use α = 0.05.

STEP 2:

Find the test statistic and P-value.

F	=
P-value	=

Find the test statistic and P-value.

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 + ...

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