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.The value of the test statistic is ____________. A) t₃₅ = -2.00 B) z = -2.00 C) t₃₅ = -0.33 D) z = -0.33

Question

Quizplus · Accepted Answer

Since the population standard deviation is known and the sample size is greater than 30, we can use a z-test. The formula for the test statistic is:
z = (x̄ - μ) / (σ / √n)
where x̄ is the sample mean, μ is the population mean (12 minutes), σ is the population standard deviation (12 minutes), and n is the sample size (36). Substituting the values given in the problem, we get:
z = (8 - 12) / (12 / √36) = -2.00
Therefore, the value of the test statistic is -2.00, which corresponds to choice B.

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