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Tasya [4]
3 years ago
14

For a population with µ = 80 and σ = 20, the Sampling distribution of the Mean, based on n = 16 will have an expected value of t

he mean = ____ and a standard error of the mean = ____
Mathematics
1 answer:
allsm [11]3 years ago
6 0

Answer:

Will have an expected value of the mean = 80 and a standard error of the mean = 5

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 80, \sigma = 20

n = 16

So the mean is 80 and the standard deviation is s = \frac{20}{\sqrt{16}} = 5

Will have an expected value of the mean = 80 and a standard error of the mean = 5

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