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I have a large dataset of vehicles's speeds. My goal is to infer an upper bound on the (average) speed of the population of all vehicles $U$

The way this is to be done is like this:
Given a potential speed bound $S$ we will test the hypothesis that $U < S$. The null hypothesis then would be: $ U >= S $

I've a rather limited statistics knowledge (I'm a programmer!) and would like to know an algorithm for accepting or rejecting an $S$.

We have no knowledge of the population of all vehicles (neither distribution nor mean).

I know I have to use z-score (it's a large dataset), but I'm having trouble figuring out what each variable in the z-score formula should correspond to in my case. I'm thinking maybe I should look at only the vehicles where $ \text{speed of vehicle} >= S$ for testing the null hypothesis, this would be the sample set, and the population would be all vehicles.

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closed as unclear what you're asking by kjetil b halvorsen, StatsStudent, Carl, Juho Kokkala, mdewey Jan 1 at 12:24

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ How would taxi speeds be representative of bus speeds? $\endgroup$ – Glen_b Dec 31 '18 at 2:28
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    $\begingroup$ Apart from the concerns about representativity, what is really the null hypothesis? Do you have postulated an upper limit? How? The legal upper speed limit, or something else? $\endgroup$ – kjetil b halvorsen Dec 31 '18 at 11:55
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    $\begingroup$ We are concerned because we know these "irrelevant" constraints are crucial to obtaining a correct answer. You're headed in an erroneous direction where no amount of theory, calculations, or programming are going to do you any good. $\endgroup$ – whuber Dec 31 '18 at 18:48
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    $\begingroup$ If you are really just interested in the upper bound on speed (and not just average speed), why not just google the fastest car in the world (among the population of all cars)? You don't even need statistics here if the answer is already well-known. It seems, for an appropraitely defined universe, U is given by 284.6 mph by the Koenigsegg Agera RS:foxnews.com/auto/… $\endgroup$ – StatsStudent Dec 31 '18 at 19:07
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    $\begingroup$ The upper bound on speed is c, the speed of light. If you find an maximum speed for a population of traveling vehicles, that is nice, but the meaning is a bit empty. Just taking the maximum of a population will do that but one typically asks for some percentage of the population that exceeds a given speed as this is more likely to be a representative number, i.e., more independent of population size. For example, 5% exceed 127 kph, or some such. I think you need to explore the goal, aim, purpose, rational usage, or form of the question before positing it. Currently, the question is unclear. $\endgroup$ – Carl Dec 31 '18 at 19:32
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From reading the comments, it becomes clear that the answer to this is "you can't".

One comment notes that there are 8 million data points and states (a bit sarcastically) that this is "enough" and then another comment says to assume that taxi speed is a random sample of all vehicles' speed.

Sample size is essentially irrelevant if the sample is biased and, despite the comment, it's not at all safe to assume that taxis are a random sample of vehicles - they are almost surely biased. Even a very small number of (say) professional race car drivers would surely raise the top speed a lot.

For an example of what can go wrong with large but biased samples, look up the Literary Digest poll of 1936 - and that was about a proportion which is easier to estimate than a maximum.

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