Bill Smith is the Worthington Township manager. When citizens request a traffic light, the staff assesses the traffic flow at the requested intersection. Township policy requires the installation of a traffic light when an intersection averages more than 150 vehicles per hour. A random sample of 48 vehicle counts is done. The results are as follows:

Sample Size = 48

Sample Mean = 158.3 vehicles/hr.

Sample Standard Deviation = 27.6 vehicles/hr.

Does the sample data provide evidence to conclude that the installation of the traffic light is warranted (using α = .10)?  Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses. 

b. State the level of significance.

c. Find the critical value (or values), and clearly show the rejection and non rejection regions.

d. Compute the test statistic.

e. Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e. What does this mean?

g. Find the observed p-value for the hypothesis test and interpret this value. What does this mean?

h. Does this sample data provide evidence (with α = 0.10), that the installation of the traffic light is warranted?