Question

2. The head of public safety notices that the average driving speed at a particular intersection averages 35 mph with a standard deviation of 7.5 mph. After a school speed limit sign of 20 mph is placed at the intersection, the first 40 cars travel past at an average speed of 32 mph. Using the .01 alpha level, was there a significant change in driving speed? a. Use the four steps of hypothesis testing. b, Sketch the distributions involved

Answer 1

the a. Use the five steps of hypothesis testing

Step 1: Restate the question as a research hypothesis and a null hypothesis about the populations

The research hypothesis is that driving speed is different after the placement of the speed sign from the mean driving speed of the population of people driving through the intersection: u1 ≠ u2.

The null hypothesis is that both populations will have the same mean speed: u1 = u2

Step 2: Determine characteristics of the comparison distribution and the critical cut-off

μM = μ = 35

σ^2M = σ^2/N = 7.5^2/40 = 56.25/40=1.406

σM = 1.185 = 1.19

Two-tailed cut-offs, 0.01 significance level are 2.58 and -2.58

Step 3: Determine sample score on the comparison distribution

Mean = 32

σM = 2

Population 1: people driving at a particular intersection

Population 2: first 40 people to travel past school zone intersection after sign is placed

Z = (M- μM)/ σM = (32-35)/2 = -1.5

Step 4: Conclusion (Accept or Reject the null hypothesis)

Z score of the sample's mean is -1.5, which is less extreme than -2.58;

Accept the null hypothesis.

And then conclude that the null hypothesis is that both populations will have the same mean speed: u1 = u2