The city's Transit Commission wants to determine if there is a need for a change in the frequency of service of a bus route. Historical data suggests that the average distance traveled by travelers in this route is 4.5 km per day. If the current mean trip distance differs from 4.5 km per day (i.e., either higher or lower than this historical average) then changes in service may be necessary. From a random sample of 38 bus riders, it is found that the sample mean is 3.9km per resident per day with a sample standard deviation of 2.1km. Is a change in service necessary?

Answer the following questions in the blanks below. Use two decimal places. [5 points]

1. What is the appropriate test statistic in this setting (z or t)? Why?
2. State the null and alternative hypothesis. (To avoid having to type subscripts or symbols, in the space provided, write your answer in words. For example null: mu equals x, alternative: mu is greater than/less than/not equal to x. On the sheet you will submit for your written work, write it out as we have been doing in class).
3. What is the value of the test statistic?
4. What is the p-value associated with the test statistic?
5. Using a level of significance of 0.01, what can you conclude? Why? (in your written work be sure to show how you are arriving at this conclusion)