Question 1196048: is it true that a statistic can never be equal to zero
Found 3 solutions by MathLover1, ikleyn, math_tutor2020:
Answer by MathLover1(20850)   (Show Source):
Answer by ikleyn(52848)  (Show Source):
You can put this solution on YOUR website! .
In her response, @MathLover1 forgot to refer to the source, from which she copied-pasted her response
https://homework.study.com/explanation/since-the-population-size-is-always-larger-than-the-sample-size-then-the-sample-statistic-a-can-never-be-larger-than-the-population-parameter-b-can-never-be-equal-to-the-population-parameter-c-can-never-be-zero-d-none-of-the-other-answers-are-correc.html#:~:text=Answer%20and%20Explanation%3A&text=A%20sample%20statistic%20can%20be,summation%20that%20is%20never%20zero.
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After post by @math-tutor2020:
In my post above, my goal was to provide the link ONLY, from which @MathLover1 copied and pasted.
My goal was not to provide an evidence.
Surely, what was written in that post was EXTREME nonsense.
I just posted a message to their site asking them to remove that writing from there.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
The answer is false. A statistic CAN in fact be zero. The link cited by the other tutor doesn't provide adequate evidence as to why a statistic cannot equal zero. Edit: My apologies @ikleyn, I misread what you meant.
Consider the population of values: {-2, -1, 1, 2, 3, 4}
Now consider a sample of these values {-1, 1} which is a subset of the population.
Compute the average to get (-1+1)/2 = 0/2 = 0
This example shows that a statistic can be equal to zero.
Recall that a parameter is something like the population mean, while the associated statistic is the sample mean.
The goal of a statistic is to estimate the parameter.
As you can probably guess, the class of statistics refers to this very idea.
For further practice, check out this sample quiz
https://vault.hanover.edu/~dodge/Statistics/MC_Quizzes/index3.html
Question 1 is very similar to this current question.
Scroll to the bottom to click for the answers, and it will show that "choice E) none of the above" is the answer for question 1.
"choice C) can never be zero" is ruled out (in that it can be zero)
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