The accompanying data show spot speeds collected at a section of highway located in a residential area before and after an increase in speed enforcement activities. Using the student’s t test, determine whether there was a statistically significant difference in the average speeds at a significance level of ? = 0.05 (the 95% confidence level). Also report, for both the before and after cases, the mean speed, standard deviation, 85th percentile speed, and percentage of traffic exceeding the posted speed limit of 30 mi/h.

Question

Answer 1

First calculate average and standard deviation for both sets of data.

The mean speeds for before and after cases will be:



Using t-test:

Calculate the pooled standard deviation for both sets of data using Eq. 4.9.



Using a T-distribution table with 58 degrees of freedom (????1 + ????2 - 2 + 30 + 30 - 2 - 58) and a significance of ???? = 0.05, a theoretical value of ????? = 1.67 is found.



Since 6.59 > 1.67, then ???? > ?????, so the null hypothesis can be rejected and it can be concluded with 95% confidence that the before speeds are greater than the after speeds.

The percentage of traffic exceeding the posted speed limit of 30 mi/h is:



The 85th percentile speed can be determined from the table below:





85th percentile speed before: between 38 and 39 mi/h

85th percentile speed after: between 33 and 34 mi/h