Question

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?Sketch the distributions involved.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Initial:

arithmetic average = 35 mph

standard deviation = 7.5 mph

Final (sign of 20 mph) :

40 cars

arithmetic average = 32 mph

alpha level = 0.01

Step 02:

Research hypothesis : u1 ≠ u2

Null hypothesis : u1 = u2

μM = μ = 35

σ²M = σ²/N = (7.5²)/40 = 56.25/40 = 1.406

σM = 1.185

0.01 significance level ===> 2.58 and -2.58

Mean = 32

σM = 2

Z = (M- μM)/ σM = (32-35)/2 = -1.5

Z score (sample's mean) = -1.5

It is less than -2.58

The answer is:

The signal does not generate a significant change in driving speed.

Null hypothesis is accepted.