A county engineer would like to determine if a speed reduction strategy has been effective, and performs a second speed study to pair with one done before the strategy was implemented. The collected data has the following characteristics. Determine, with a 95% confidence level, if there is a statistically significant decrease in speeds, using first the t-test and then the Z-test.

Question

?1 = 43.8 mi/h ? 2 = 35.2 mi/h
S1 = 6.5 mi/h S2 = 7.6 mi/h
n1 = 30 n2 = 30

What will be an ideal response?

Answer 1

Determining significance in a “decrease” in speeds indicates a one-tail test. For the t-test, first compute the square root of the pooled variance, using Eq. 4.9.
Sp2 = ((n1 - 1)S12 + (n2 - 1)S22) / (n1 + n2 - 2)
Sp = 7.1
Now find the test statistic T using Eq. 4.8.
T = 4.69
Determine the t-value, 30 + 30 – 2 = 58 degrees of freedom, t = approximately
1.671.
Since 4.69 > 1.671, T > t and it can be concluded that there is a significant decrease in speeds.
Using the Z-test, determine the standard deviation of the difference in means, using Eq. 4.7.
Sd = 1.825
The z-value for 95% confidence is 1.645. The test for significance is thus SdZ = 1.825 x 1.645 = 3.002.
Since the difference in means (43.8 – 35.2) = 8.6 > 3.002, it can be concluded that there is a significant decrease in speeds.