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.)

school, with four levels

education level, with three levels

education level, with four levels

media usage, with two levels

media type, with five 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 ? = 0.05.

STEP 1:	State the hypotheses. H0:  ---Select One--- All types of media have different population mean indices. At least two types of media have different population mean indices. No difference in population mean index according to education level. All education levels have different mean indices. At least two education levels have different mean indices. No difference in population mean index by media type. H1:  ---Select One--- At least two types of media have different population mean indices. No difference in population mean index according to education level. 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. All education levels have different mean indices.
STEP 2:	Find the test statistic and P-value. F = P-value =
STEP 3:	State your conclusion. At the 5% level of significance,  ---Select--- do not reject/reject H0 for education level. The data  ---Select--- do not indicate any difference/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 ? = 0.05.

STEP 1:	State the hypotheses. H0:  ---Select One--- No difference in population mean index by media type. All education levels have different mean indices. No difference in population mean index according to education level. All types of media have different population mean indices. At least two types of media have different population mean indices. At least two education levels have different mean indices. H1:  ---Select One--- No difference in population mean index according to education level. At least two types of media have different population mean indices. No difference in population mean index by media type. 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.
STEP 2:	Find the test statistic and P-value. F = P-value =
STEP 3:	State your conclusion. At the 5% level of significance,  ---Select One--- reject/do not reject H0 for media. The data  ---SelectOne--- do not indicate any differences/indicate differences in population mean index according to media type.

Answer 1

Solution :--

(a) List the factors and the numbers of levels of each facor .

Education level , with four levels.

(i.e Educational Level - less than high school , High school graduate , Some College , College Graduate ).

Media type , with five levels .

(i.e. Media Type - Cable Network, Prime_Time TV , Radio , Nespaper , Magzine )

(b) Population mean index based On education.

1). Hypothesis --

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

and ,

H₁ : At least two education levels have different mean indices.

2). Test Statistics and P- value :-

F = 2.96

P- Value = 0.075

3). Conclusion :

  At 5% level of significance ,   

We do not reject Ho for eduactional level .

  We conclude that , No difference in population mean index according to education level.

( c ) population mean index based on media :

1). Hypothesis :  

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

and

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

2). Test Statistic and p-value :

F = 0.01

p-value = 1.000

3). Conclusion :

At 5% level of significance ,   

  

We do not reject Ho for eduactional level .

  We conclude that , No difference in population mean index by media type .