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 5,2011).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 runs were 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 a population standard deviation for bus arrival time of 12 minutes.At the 1% significance level,does the evidence support the Boston public schools' claim?
A) No,because the p-value is greater than α.
B) Yes,because thep-value is greater than α.
C) No,because the value of the test statistic is less than the critical value.
D) Yes,because the value of the test statistic is less than the critical value.

Question

Quizplus · Accepted Answer

The null hypothesis is that the mean lateness is 12 minutes. The alternative hypothesis is that the mean lateness is less than 12 minutes. Using a z-test, the test statistic is calculated as (8-12)/(12/sqrt(36)) = -2. The critical value for a 1% significance level (one-tailed) is approximately -2.33. Since -2 is greater than -2.33, we fail to reject the null hypothesis. The p-value is greater than 0.01, so there is not enough evidence to support the claim.

The Boston Public School District Has Had Difficulty Maintaining On-Time