Question

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

(a) List the factors and the number of levels of each factor. (Select all that apply.)

media usage, with two levels

education level, with three levels

media type, with five levels

education level, with four levels

school, with four levels

media type, with four levels

(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 = 0.1.

STEP 1:	State the hypotheses. H0:  ---Select--- No difference in population mean index according to education level. At least two education levels have different mean indices. All education levels have different mean indices. At least two types of media have different population mean indices. All types of media have different population mean indices. No difference in population mean index by media type. H1:  ---Select--- All education levels have different mean indices. At least two education levels have different mean indices. No difference in population mean index according to education level. At least two types of media have different population mean indices. All types of media have different population mean indices. No difference in population mean index by media type.
STEP 2:	Find the test statistic and P-value. F = P-value =
STEP 3:	State your conclusion. At the 10% level of significance,  ---Select--- do not reject OR reject H0 for education level. The data  ---Select--- do not indicate any differences OR indicate differences in population mean index according to education level.

(c) Determine if there is a difference in population mean index based on media. Use α = 0.1.

STEP 1:	State the hypotheses. H0:  ---Select--- At least two types of media have different population mean indices. All education levels have different mean indices. All types of media have different population mean indices. At least two education levels have different mean indices. No difference in population mean index by media type. No difference in population mean index according to education level. H1:  ---Select--- No difference in population mean index by media type. No difference in population mean index according to education level. All types of media have different population mean indices. All education levels have different mean indices. At least two education levels have different mean indices. At least two types of media have different population mean indices.
STEP 2:	Find the test statistic and P-value. F = P-value =
STEP 3:	State your conclusion. At the 10% level of significance,  ---Select--- do not reject OR reject H0 for media. The data  ---Select--- do not indicate any differences OR indicate differences in population mean index according to media type.

Answer 1

(a)

media type, with five levels

education level, with four levels

(b) STEP-1

For difference testing, we assume null hypothesis as there is no difference between means and for alternate hypothesis, we assume that at least two levels are different

Ho: No difference in population mean index according to education level.

Ha: At least two education levels have different mean indices.

STEP-2 using the given data output table

we get

F = 2.96

p value = 0.075

STEP 3:- p value is less than 0.10 level of significance, rejecting the null hypothesis.

At the 10% level of significance, reject H₀ for education level.

The data   indicate differences in population mean index according to education level.

(C) STEP 1

H₀:  No difference in population mean index by media type.

H₁:  At least two types of media have different population mean indices

STEP-2 using the given data output table

we get

F = 0.01

p value = 1.000

STEP 3:- p value is greater than 0.10 level of significance, failing to reject the null hypothesis.

At the 10% level of significance,  do not reject H₀ for media.
The data do not indicate any differences in population mean index according to media type.