Dependent vs Independent sample

Question

I am quite confused about a question that came up in my exam.

Question: The travel times on two alternative routes through a network are recorded on 20 working days during a month. The results of this are given in Table 4. Perform an appropriate hypothesis test to investigate the difference between the mean travel times on the two routes, and comment on the outcome of this.

I initially believed the samples would be independent, however my peers have said they are dependent.

EDIT    adding the data table from comments:

     Route
Day 1  2
1 401 420
2 433 451
3 355 378
4 436 456
5 580 616
6 497 549
7 401 433
8 413 430
9 353 368
10 449 480
11 341 369
12 402 413
13 423 441
14 438 462
15 358 361
16 470 489
17 392 420
18 369 387
19 394 417
20 368 385

Table 4: travel times (seconds) Day Route 1 2 1 401 420 2 433 451 3 355 378 4 436 456 5 580 616 6 497 549 7 401 433 8 413 430 9 353 368 10 449 480 11 341 369 12 402 413 13 423 441 14 438 462 15 358 361 16 470 489 17 392 420 18 369 387 19 394 417 20 368 385 — HelpIsNeeded, Apr 27 '17 at 18:50
Edit your question to put the table in the question itself, with appropriate formatting. — Kodiologist, Apr 27 '17 at 18:51
This isn't really a question about the numbers: it invites you to think about how the travel times might influence each other *or be influenced by common factors*. That requires some combination of common sense and imagination, nothing more. — whuber, Apr 27 '17 at 18:52
It seems to me that if there are some common parts in the two routes that could cause the dependence. To help further you may want to show Table 4. Also the question should have the self-study tag. Are there other factors that are considered in the problem such as time of day? — Michael R. Chernick, Apr 27 '17 at 18:52
Thats all the information given. From the table, im kind of struggling to get a decent formatting for it, but times on route 2 are generally higher than route 1. That being said, there's no indication to the sampling strategy used or the type of routes. — HelpIsNeeded, Apr 27 '17 at 19:00
[Related](https://stats.stackexchange.com/questions/137337/plain-language-meaning-of-dependent-and-independent-tests-in-the-multiple-co). — Alexis, Jun 16 '20 at 15:45

score -2 · Answer 1 · answered Apr 27 '17 at 20:05

-2

If it is the same driver in the same car on the travelling both routes over 20 days then the samples are dependent. If there are different drivers in different cars on the two routes then the samples are independent. Samples can only be dependent if there is some common factor, like a single driver, otherwise the samples are independent

answered Apr 27 '17 at 20:05

Kgomotso Lekola

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I'm afraid this just isn't so. As comments by @Michael Chernick have suggested, many factors could influence both sets of data, including common segments along their routes, meteorological conditions, and much more. "Independent" has a clear definition in terms of relationships among probabilities: it is not solely determined by common factors you might (or might not) recognize. – whuber Apr 27 '17 at 20:15
There's nothing in the question to suggest any of the aspects you are putting forward. You are going deep into conjecture. This is a simple and straightforward question. – Kgomotso Lekola Apr 27 '17 at 21:00
On the contrary: this is a subtle and probably unanswerable question as stated. I think it incontrovertible, though, that your answer is incorrect, as simple counterexamples will show (such as those already suggested by Dr. Chernick). – whuber Apr 27 '17 at 21:18

Dependent vs Independent sample

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