The Boston public school district has had difficulty maintaining on$-$time bus service for its students $("$A Year Later, School Buses Still Late," Boston Globe, October $5).$ Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, $12$ minutes late. After the schedule adjustment, the first $36$ bus runs showed an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement$-$students were not as late. Assume the population standard deviation for bus arrival time was $12$ minutes. At the $5\%$ significance level, the decision is

Multiple Choice

reject $H_{}$; we can conclude that the schedule adjustment was an improvement

reject $H_0,$ we cannot conclude that the schedule adjustment was an improvement

do not reject $H_0$ we can conclude that the schedule adjustment was an improvement