14.55 An analyst conducted a survey and found that the respondents can be categorized into three broad categories professionals, speeders, and posers by three age groups of Group 1: 21 to 30 years, Group 2: 31 to 40 years, and Group 3: 41 to 50 years. The categorizations are as follows:

Group 1 Group 2 Group 3 Professionals 18 41 39 Speeders 47 30 40 Posers 15 26 13 Do these data indicate that there is a difference in respondents’

categories for the three age groups? Test on a 5% significance level.