The __________ of the sample mean, x̄, is the probability dist...

Question

The __________ of the sample mean, x̄, is the probability distribution of all possible values of the random variable x̄ computed from a sample of size n from a population with mean μ and standard deviation σ.

Accepted Answer

Hello there. Today we are going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Which term best names the probability distribution of all possible sample means of size n from a population with parameters mu and sigma. OK, so it appears for this particular problem we're asked to look at our multiple choice answers and we're asked to determine which term stated in our multiple choice answers best names the probability distribution of all possible sample means of size lowercase n from a population with parameters mu and sigma. OK, so now that we know what we're ultimately trying to solve for, let's take a moment to read off our multiple choice answers to see what our final answer may be. So A is sample selection distribution, B is measurement error distribution, C is population density function, and D is sampling distribution of the mean. OK. So our first step that we need to take is we need to recall and state the mean property formula, and the mean property formula states that mu subscript X bar is equal to mu. Our second step is we need to recall and state the standard error formula, which states that sigma subscript X bar is equal to sigma divided by the square root of N. Our third step now is we need to recall and state the central limit theorem condition, which is, for this case, if the population is normal or lower case n. is larger than X bar, meaning it is approximately normal with the parameters above, meaning, for example, X bar is approximately of mu sigma divided by the square root of lower case n. That will mean that undeniably for our 4th step, we will be able to recall and recognize that the object by definition will be that this particular prom is describing a sampling distribution of. The mean. So that means that our correct and final answer based on our, our prior knowledge and what we determined together, our correct and final answer will be multiple choice answer letter D, which once again is sampling distribution of the mean. And that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

The __________ of the sample mean, x̄, is the probability distribution of all possible values of the random variable x̄ computed from a sample of size n from a population with mean μ and standard deviation σ.

Key Concepts

Sampling Distribution

Sample Mean (x̄)

Population Parameters (μ and σ)

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