Question

A city councilwoman is concerned that the new contractor she hired is taking too long to replace defective streetlights. She would like to perform a hypothesis test to determine if the replacement time for streetlights under the new contractor is in fact longer than the replacement time under the previous contractor, which was 3.2 days on average. She selects a random sample of 12 streetlight service calls and obtains the following times to replacement (in days). Use a significance level of 0.05.

6.2 7.1 5.4 5.5 7.5 2.6 4.3 2.9 3.7 0.7 5.6 1.7

1. Define in the context of the problem and state the appropriate hypotheses.
2. Does the data come from a normal distribution? Why or Why not?
3. Calculate the appropriate test statistic by hand. Write out all your steps.
4. What is your decision regarding the null hypothesis?
5. What is your conclusion? (In other words, write the final summary statement.

Answer 1

a) H0: The new contractor is in fact not longer than the replacement time under the previous contractor

H1: The new contractor is in fact longer than the replacement time under the previous contractor

b) The probability plot from MINITAB is

Here P-value > 0.05 so we conclude that the sample data follows normal distribution

c)

Critical t: 1.7959
P-Value: 0.0361

Here t value > t critical value and P-value < alpha 0.05 so we reject H0

thus we conclude that the new contractor is in fact longer than the replacement time under the previous contractor