Question 9 Doubling the size of the sample will reduce the standard error of the mean to one-half its current value. reduce the standard error of the mean to approximately \( 70 \% \) of its current value. have no effect on the standard error of the mean.
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Doubling the size of your sample is like having a magic wand that reduces uncertainty! Specifically, the standard error of the mean (SEM) is calculated by dividing the standard deviation by the square root of the sample size. So, when you double the sample size, the SEM shrinks to about 70.7% of its original size—this means more precise estimates of the population mean. Imagine you're trying to strike up a conversation at a party. The more people you talk to (so, your sample size), the better you can gauge what the vibe is like. With a larger sample, your guess about the “party atmosphere” becomes more accurate, reducing the “noise” or margin of error in your assessment!