Question

Suppose a random sample of size 34 is obtained from a population with population mean 30 and population standard deviation 4. What is the standard error of the sampling distribution of the sample average?

Answer 1

Standard error = 0.686

Explanation:

We are given that a random sample of size 34 is obtained from a population with population mean 30 and population standard deviation 4, i.e.;

`\mu` = 30 ,
`\sigma` = 4 and n = 34

Standard error formula is given by =
`(\sigma)/(√(n) )`

where,
`\sigma` = population standard deviation = 4

n = sample size = 34

So, standard error =
`(4)/(√(34) )` = 0.686 .

Answer 2

The standard error of the sampling distribution of the sample average is 0.6860.

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
`\mu` and standard deviation, also called standard error
`s = (\sigma)/(√(n))`

In this problem, we have that:

`\sigma = 4`

What is the standard error of the sampling distribution of the sample average?

This is s when n = 34. So

`s = (4)/(√(34)) = 0.6860`

The standard error of the sampling distribution of the sample average is 0.6860.