Examining medical data relative to students in the elementary school she directs, Miss Carter, the principal, noted that 200 students missed at least 5 days of school when they were 10 and 12; 165 students missed at least 5 days of school at 10 years of age but not at 12 years of age; 235 students missed at least 5 days of school at 12 years of age but not at 10, and 600 did not miss days of school neither at 10 nor at 12 years of age. Conduct a statistical analysis to test whether there was a significant change in how often students got sick at 10 and 12 years of age. State the null and alternative hypothesis, calculate the test statistic, and state your decision and conclusion.