Question: An analyst hypothesizes that the Peter Principle can be demonstrated by examining the competency and rank of the teaching staff at X university. (The Peter Principle states that people rise in an organization until they reach their level of incompetence.) If true for the University, there should be proportionately more competent people at the lower ranks. To test this hypothesis, students are asked to rate each teacher at the school. The analyst calculates the chi-square statistic based on the data shown in the table below. She obtains a value of 76.42. Based on this result, what conclusion can she draw? Explain your answer.

a. State the null and alternative hypotheses:

b. Using the chi-square statistics cited above, test the null hypothesis at the 5% significance level

c. Using the data in the table above in SPSS, perform the chi-square procedure to test the null hypothesis at the 5% significance level. Explain how the SPSS output can be used to accept or reject the null hypothesis. Show the SPSS output.