Difference of Two Population Proportions (Setup) Practice Test

A city compares two methods for repairing potholes to see which results in fewer repairs needed within 6 months. For Method A, 19 of 85 repaired potholes needed another repair within 6 months. For Method B, 10 of 80 repaired potholes needed another repair within 6 months. The city’s research claim is that Method A has a higher proportion needing another repair than Method B. Which hypotheses are appropriate for testing this claim about the population proportions?

An engineer tests whether a new manufacturing process changes the proportion of parts that are defective. Under the old process, 17 of 220 randomly selected parts are defective. Under the new process, 29 of 210 randomly selected parts are defective. The engineer’s research claim is that the defect proportion is different under the new process than under the old process. Which hypotheses are appropriate for testing this claim?