Question description

 

Ms. Jessica Melon, a senior level official in the personnel division of a large federal office, is disturbed by the level of incompetence she perceives in the leadership of the organization. She is convinced that incompetence rises to the top. To substantiate her claim, she intends to conduct an analysis. She selects from her personnel files a random sample of 200 people employed by the organization. Form the formal education and civil service examination scores of these people, she classifies them into two levels of competence (low or high), and from their General Schedule ratings and formal job descriptions, she classifies them into three categories of hierarchical position in the organization (low, medium, or high). The cross-tabulation of these two variables for the sample of employees as follows. Ms. Jessica Melon would like to know whether she can legitimately infer from this sample cross-tabulation that a relationship exists between competence and hierarchical position in the population of all workers in the organization. She decides to perform the chi-square test. She intends to write a policy memo to Ms. Julie Casey, the Director of the federal office regarding her analysis and its findings.

Â	Competence
Hierarchy	Low	High	Total
Low	80	20	100
Medium	45	15	60
High	25	15	40
Total	150	50	200

 

What is the conclusion ? Did you answer the question using the appropriate statistic and interpret the statistic correctly?