Estimate margins of error for the sample mean using a bootstrap

returns results through the frontend and adds some fields to the backend response
The unit of observation is the "one hour average" which, while not statistically valid, should be a decent starting point, and demonstrates how margins of error can be calculated from a sample of observations

backend/app/get_travel_time.py

@@ -2,7 +2,7 @@
 
 from app.db import getConnection
 from app.get_links import get_links
-import numpy, math
+import numpy, math, random
 
 # the way we currently do it
 def mean_daily_mean(obs):
@@ -87,8 +87,30 @@ def get_travel_time(start_node, end_node, start_time, end_time, start_date, end_
 
     tt_seconds = mean_daily_mean(sample)
 
+    reported_intervals = None
+    if len(sample) > 1:
+        # bootstrap for synthetic sample distribution
+        sample_distribution = []
+        for i in range(0,100):
+            bootstrap_sample = random.choices( sample, k = len(sample) )
+            sample_distribution.append( mean_daily_mean(bootstrap_sample) )
+        p95lower, p95upper = numpy.percentile(sample_distribution, [2.5, 97.5])
+        reported_intervals = {
+            'p=0.95': {
+                'lower': timeFormat(p95lower),
+                'upper': timeFormat(p95upper)
+            }
+        }
+
     return {
-        'results': {'travel_time': timeFormat(tt_seconds)},
+        'results': {
+            'travel_time': timeFormat(tt_seconds),
+            'confidence': {
+                'sample': len(sample),
+                'intervals': reported_intervals
+            },
+            'observations': [timeFormat(tt) for (dt,tt) in sample]
+        },
         'query': {
             'corridor': {'links': links},
             'query_params': query_params

frontend/src/travelTimeQuery.js

@@ -64,6 +64,8 @@ export class TravelTimeQuery {
         record.set('hoursInRange', this.hoursInRange)
         record.set('mean_travel_time_minutes', this.#results?.travel_time?.minutes)
         record.set('mean_travel_time_seconds', this.#results?.travel_time?.seconds)
+        record.set('moe_lower_p95', this.#results?.confidence?.intervals?.['p=0.95']?.lower?.seconds)
+        record.set('moe_upper_p95', this.#results?.confidence?.intervals?.['p=0.95']?.upper?.seconds)
 
         if(type=='json'){
             return Object.fromEntries(record) // can't JSONify maps