Question

Suppose the average math SAT score for students enrolled at local community college is 490.4 with a standard deviation of 63.7. A random sample of 49 students has been selected. The standard error of the mean for this sample is __________

Answer 1

The standard error of the mean for this sample is 9.1

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, which is also called standard error of the mean,
`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 problem, we have that:

`\sigma = 63.7, n = 49`

So

`s = (63.7)/(√(49)) = 9.1`

The standard error of the mean for this sample is 9.1