Determine whether the statement is true or false. If it is fal...

Question

Determine whether the statement is true or false. If it is false, rewrite it as a true statement.

A sample statistic will not change from sample to sample.

Accepted Answer

Hello there. Today we're 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. Can a sample statistic vary when taking different samples from the same population? Explain why or why not? Awesome. So it appears for this particular prong we're asked to determine whether or not can a sample statistic vary when taking different samples from this within the same population, and then we're asked to explain why or why not we can do this. So now that we know what we're trying to solve for, let's take a moment to read off all of our multiple choice answers to see what our final answer might be. A is no, because once calculated, a sample statistic is always the same. B is no because the sample statistic remains constant regardless of the sample. C is yes because each sample may include different members from the population. And finally, D is yes, because the population changes every time a sample is taken. Awesome. So first off, let us recall and define what the definition of a sample statistic. So as you should recall, a sample statistic is a numerical value derived from a sample such as the mean or proportion that is used to estimate a population parameter. So let's take a moment to quickly recall that a sample is a. Select group from a larger population. So let's say the population is 200, and if we were to take a sample of the overall population, the sample would be 40 out of the 200 instead of it being the entire population, which is 200. So with that in mind, let us also recall and note what happens with variation in sample statistics. And yes, we need to recall that a sample statistic can vary when taking different samples from the same population. And the reason for this is, as we should recall, sampling variability. So when different random samples from the same population can include different individuals which will, as a result, lead to variations in the calculated statistics. So. There is sampling variability because different random samples from the same population overall can include different individuals which leads to once again leads to variation in the calculated statistic. And we also have to consider and recall the randomness factor, and the inherent randomness in selecting individuals means that each sample may yield slightly different results, and an example of this is we need when we calculate. So once again, an example would be when calculating the average height from two different samples of the same population overall, which may result in slightly different averages. So with that in mind, therefore, in conclusion, variations in sample statistics occur because the samples may differ in comparison even when drawn from the same population. So with that said, our final answer without a doubt has to be multiple choice answer letter C, which is yes. Because each sample may include different members from the population, 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.

Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A sample statistic will not change from sample to sample.

Key Concepts

Sample Statistic

Sampling Variability

True Statement Revision

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