Statewide, the police clear by arrest 35% of the robberies and 42% of the aggravated assaults reported to them. A researcher takes a random sample of all the robberies (N = 207) and aggravated assaults (N = 178) reported to a metropolitan police department in one year and finds that 83 of the robberies and 80 of the assaults were cleared by arrest.
Are the local arrest rates significantly different from the statewide rate? Write a sentence or two interpreting your decision.