# Confidence Intervals WS #3

```Confidence Intervals WS #3
1a) Assumptions:
 Given an SRS of flights
 Distribution is approx. normal because boxplot is approx. symmetrical.
  unknown
s 
 3.675 
x  t * 
  (52.069,56.331)
  54.2  1.833
 n
 10 
We are 90% confident that the true mean airborne time is between 52.1
minutes and 56.3 minutes.
b) Since airlines are rated on whether flights arrive on-time or not, I would
use the upper bound of the interval and publish an arrival time of 10:57 a.m.
2a) Assumptions (for all three):
 Given SRS of triathletes
 Given heart rate is approx. normal
 ’s unknown
Swimming: (182.47, 193.53) We are 95% confident that the true mean
heart rate of the triathletes for swimming is 182.5 bpm to 193.5 pbm.
Biking:
(179.47, 192.53) We are 95% confident that the true mean
heart rate of the triathletes for biking is 179.5 bpm to 192.5 pbm.
Running:
(188, 200) We are 95% confident that the true mean heart
rate of the triathletes for running is 188 bpm to 200 pbm.
b) Since all three intervals overlap each other, there is not sufficient
evidence to conclude that the mean maximum heart rate is higher for
running than the other two events.
 1 
.1  1.96

3)
 n
n  385 issues
```
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