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. MediaIncome LevelCableNetworkPrime-TimeTVRadioNewspaperMagazineLess than $20,00078112898091$20,000-$39,9999710510097100$40,000-$74,99911392106111105$75,000 or more12194107121105Source: From American Demographics, Vol. 17, No. 6. Reprinted with permission, copyright 1995 American Demographics, Ithaca, NY.Minitab Printout for Media/Income DataAnalysis of Variance for IndexSourceDFSSMSFPIncome 310783592.770.088Media 4 15 40.030.998Error121558130 Total192651 (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=

(b) The null and alternative hypotheses are;Null hypothesis: There is no difference in population…

Answered: In a study of media usage versus…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4BGP

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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	Cable Network	Prime-Time TV	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	=

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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