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, 17 minutes late. After the schedule adjustment, the first 25 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 17 minutes. The value of the test statistic is __________.Multiple Choicez = −0.33t35 = −0.33t35 = −2.65z = −2.65
Question
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, 17 minutes late. After the schedule adjustment, the first 25 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 17 minutes. The value of the test statistic is __________.Multiple Choicez = −0.33t35 = −0.33t35 = −2.65z = −2.65
Solution
The question is asking for the value of the test statistic in a hypothesis test. The test is comparing the mean of a sample (the average lateness after the schedule adjustment) to the mean of a population (the historical average lateness).
The formula for the test statistic in a z-test is:
z = (X̄ - μ) / (σ / √n)
where:
- X̄ is the sample mean (8 minutes)
- μ is the population mean (17 minutes)
- σ is the population standard deviation (17 minutes)
- n is the sample size (25 bus runs)
Substituting these values into the formula gives:
z = (8 - 17) / (17 / √25) = -9 / (17 / 5) = -9 / 3.4 = -2.65
So, the value of the test statistic is z = -2.65.
Similar Questions
Shuttle bus which links the Clayton campus to the Caulfied campus starts operating at 5:00 am and will have a service every half hour. Suppose that none of the seats on the bus are completely occupied and that there is always some room for passengers. A student who wants to travel to Caulfied arrives at the bus stop at a (uniform) random time between 8:45 am and 9:45 am. What is the probability that he/she waits at most 10 minutes? Write down your answer to an accuracy of 2 decimal points.
Imagine you want to convince the local school board that changing the high school start time from 7:10 a.m. to 8:30 a.m. would benefit all students. Which appeal would most likely move this audience to support your cause?A.Studies show that teenagers' bodies have a biological drive to stay awake fairly late at night, so early start times lead to a constantly overtired student population.B.I consulted the records in the office, and they show that 75 percent of the students at our school arrived late to at least one class in the last semester.C.You probably don't remember how hard it is for young people to get up early, but I am a teenager, and I'm telling you, it's practically impossible.D.It frustrates my parents when I sleep through my alarm and have to ask them to drive me to school — but this situation would not occur with a later start time.
Imagine you want to convince the local school board that changing the high school start time from 7:10 a.m. to 8:30 a.m. would benefit all students. Which appeal would most likely move this audience to support your cause?A.Studies show that teenagers' bodies have a biological drive to stay awake fairly late at night, so early start times lead to a constantly overtired student population.B.I consulted the records in the office, and they show that 75 percent of the students at our school arrived late to at least one class in the last semester.C.You probably don't remember how hard it is for young people to get up early, but I am a teenager, and I'm telling you, it's practically impossible.D.It frustrates my parents when I sleep through my alarm and have to ask them to drive me to school — but this situation would not occur
Brooke rides the bus 44 minutes every day.Let d represent the number of days and m represent the total number of minutes Brooke spends on the bus.Complete the table using the relationship between d and m.d m1 3 7 10 Submit
The post office, which has separate lines at different windows, determines that the standard deviation for customer waiting times on Friday afternoons is 7.2 minutes. The post office decides to experiment with a single, main waiting line. For a random sample of 25 customers, it is found that the waiting times have a standard deviation of 3.5 minutes on a Friday afternoon. At a 5% significance level, the post office wants to test the assertion that a single line results in less variation in waiting times for customers. Give your conclusion.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.