In a study of media usage versus education level an index wa

In a study of media usage versus education level, an index was used to measure media usage, where a measurement of 100 represents the US average. Values above 100 represent above average media usage.

                                      Cable       prime

Education Level          Network     Time TV     Radio     Newspaper    Magazine

Less than High School     80         112              87             76                 85

High School Grad            103        105             100            99                101

Some College                  107        94               106            105               107

College Grad                    108        90              106            116                108

Assume that there is no interaction between the factors. Use a two-way ANOVA and the following Minitab Printout to determine if there is a difference in population mean index based on education. Use = 0.1

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. The P-value is greater than the level of significance and so we fail to reject the null hypothesis that there is no difference in the population mean index according to education level. At 0.1 level of significance, we conclude that at least two education levels have equivalent mean indices.

B. The P-value is less than the level of significance and so we reject the null hypothesis that there is no difference in the population mean index according to education level. At 0.1 level of significance, we conclude that at least two education levels have different mean indices.

C. The P-value is greater than the level of significance and so we reject the null hypothesis that there is no difference in the population mean index according to education level. At 0.1 level of significance, we conclude that at least two education levels have equivalent mean indices.

D. The P-value is less than the level of significance and so we reject the null hypothesis that there is no difference in the population mean index according to education level. At 0.1 level of significance, we conclude that at least two education levels have equivalent mean indices.

E. The P-value is less than the level of significance and so we fail to reject the null hypothesis that there is no difference in the population mean index according to education level. At 0.1 level of significance, we conclude that at least two education levels have equivalent mean indices.

Solution

Given significance level = 0.1 and p-value = 0.075. since p-value is less than 0.1, reject the null hypothesis and correct option is:

B. The P-value is less than the level of significance and so we reject the null hypothesis that there is no difference in the population mean index according to education level. At 0.1 level of significance, we conclude that at least two education levels have different mean indices.