A psychologist surveys random samples of 100 students from each of three types of school (public, private and charter) about their level of academic pressure (low, moderate, high or overwhelming). A chi-square test for homogeneity gives with a p-value of about 0.005. Which of the following statements are true?
I. The test has degrees of freedom.
II. At the 0.05 level, there is convincing evidence that the distribution of pressure levels differs for at least one type of school.
III. A confidence interval for the difference between two school types in the proportion reporting overwhelming pressure could help show where the distributions differ.