QuestionWhen the population mean is known, then
Select one:
a. We used the population mean to estimate the sample SD
b. We used the sample SD to estimate the population mean
c. We used the sample mean to estimate the population mean
d. None of the above
Studdy Solution
STEP 1
What is this asking?
Which statement correctly describes how we use sample data when we already *know* the true population mean?
Watch out!
Don't mix up *sample* and *population*!
It's easy to get them twisted, so keep your eyes peeled!
STEP 2
1. Understand Population Mean
2. Understand Sample Mean
3. Relate Sample and Population
STEP 3
Let's imagine we're talking about the average height of *all* giraffes in the world.
That's a lot of giraffes!
This overall average is called the **population mean**.
STEP 4
Now, imagine we measure the height of a smaller group of giraffes, say giraffes.
The average height of *this group* is the **sample mean**.
STEP 5
We use the **sample mean** to *estimate* the **population mean**.
Think of it like this: we can't measure *every* single giraffe, so we use our smaller group to make an educated guess about the average height of *all* giraffes.
STEP 6
The question says we *already know* the **population mean**.
So, we *don't* need to estimate it!
We might use the sample mean to learn other things, but we definitely don't need it to estimate something we already know.
STEP 7
We *never* use the population mean to estimate the sample standard deviation.
The sample standard deviation tells us how spread out the heights are in our *sample* of giraffes.
It's calculated directly from the sample data.
STEP 8
We also *never* use the sample standard deviation to estimate the population mean.
The sample standard deviation tells us about the *spread* of our sample, not the average height of the entire population.
STEP 9
The correct answer is **c.
We used the sample mean to estimate the population mean**.
But, since the problem states that the population mean is *known*, the correct answer is actually **d.
None of the above**!
We don't need to estimate what we already know!
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