Exhibit 9-3.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 8 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. Refer to Exhibit 9-3.At the 5% significance level,does the evidence support the Boston public school district's claim?
A)No,since the p-value is less than α.
B)Yes,since the p-value is less than α.
C)No,since the value of the test statistic is greater than the critical value.
D)Yes,since the value of the test statistic is greater than the critical value.

Question

Quizplus · Accepted Answer

We need to conduct a one-sample t-test to determine if the mean bus arrival time after the schedule adjustment is significantly different from the historical average of 12 minutes late. The null hypothesis is that the mean arrival time is still 12 minutes late, while the alternative hypothesis is that the mean arrival time is less than 12 minutes late (improved).

Using a one-tailed t-test with a 5% significance level and 35 degrees of freedom (36-1=35), we find the critical value to be -1.6909. The test statistic is calculated as:

t = (8 - 12) / (12 / sqrt(36)) = -3.00

From a t-table with 35 degrees of freedom, the p-value is less than 0.005. Since this p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the claim that the schedule adjustment has improved bus arrival time. Therefore, the best choice is B.