Question

Suppose a random sample of 80 measurements is selected from a population with a mean of 25 and a variance of 200. Select the pair that is the mean and standard error of x.

a) [25, 2.081]
b) [25, 1.981
c) [25, 1.681]
d) [25, 1.581]
e) [80. 1.681]
f) None of the above

Answer 1

d) [25, 1.581]

Explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation(which is the square root of the variance)
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation, which is also standard error,
`s = (\sigma)/(√(n))`.

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

In this question:

`\sigma = √(200), n = 80`

So the standard error is:

`s = (√(200))/(√(80)) = 1.581`

By the Central Limit Theorem, the mean is the same, so 25.

The correct answer is:

d) [25, 1.581]