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emmainna [20.7K]
3 years ago
9

A population has a standard deviation of 5.5. What is the standard error of the sampling distribution if the sample size is 81?

Mathematics
1 answer:
VladimirAG [237]3 years ago
4 0

Answer:

\sigma = 5.5

And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution \bar X and for this case we know that the distribution is given by:

\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})

And the standard error would be:

\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}

And replacing we got:

\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611

Step-by-step explanation:

For this case we know the population deviation given by:

\sigma = 5.5

And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution \bar X and for this case we know that the distribution is given by:

\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})

And the standard error would be:

\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}

And replacing we got:

\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611

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