Question

The accompanying data show spot speeds collected at a section of highway located in a residential area. (i) Using the student’s t test, determine whether there was a statistically significant difference in the average speeds at the 95% confidence level. (ii) Also report for before and after the following: mean speed, standard deviation, 85^th percentile speed and percentage of traffic exceeding the posted speed limit of 30 MPH. (iii) using the data, draw the histogram frequency distribution, cumulative percentage distribution for each set of data and determine: (a) average speed (b) 85^th percentile speed, (c) 15^th percentile speed, (d) mode (e) median and (f) pace[the most common 10 MPH range].

Before	After
40	23
35	33
38	25
37	36
33	37
30	34
31	25
35	28
35	24
40	31
33	24
35	20
36	21
38	28
38	25
35	21
30	35
30	30
38	33
39	21
35	28
36	23
35	22
33	27
31	20
36	24
35	30
33	32

Answer 1

Given that the speed limit is 30 MPH. 85 percentile of the vehicles are crossing the speed limit, and even the 15 percentile of the cars are traveling with a speed of 31.1 MPH, which is more than the restricted rate.

After the precautionary measures, the 85th percentile speed is 33 MPH, and the 15th percentile is 21.05 MPH, which is lesser than the speed limit. So the preventive measures taken were useful,

The confidence interval also says that the speed of the vehicles is within the speed limit (30MPH) with 95% confidence.

Using the t-test the confidence limit with 95% confidence is

For getting the descriptive statistics, in excel select the data option and then descriptive statistics in the data analysis toolbox and select the input range and the output range. and select summary statistics and click ok

For getting the frequency distribution in the data analysis toolbox select the histogram and select the input range and the output range also select the cumulative distribution.

I hope you have understood.

Please do mention in the comments section for further queries.

Good Luck.!