Question

7.2.8 Scientists at the Hopkins Memorial Forest in western Mas- sachusetts have been collecting meteorological and environmen- tal data in the forest data for more than 100 years. In the past few years, sulfate content in water samples from Birch Brook has averaged 7.48 mg/L with a standard deviation of 1.60 mg/L. a. What is the standard error of the sulfate in a collection of 10 water samples

Answer 1

The standard error of the sulfate in a collection of 10 water samples is of 0.506 mg/L.

Explanation:

Central Limit Theorem

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 error
`s = (\sigma)/(√(n))`.

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

Standard deviation of 1.60 mg/L.

This means that
`\sigma = 1.6`

Collection of 10 samples:

This means that
`n = 10, s = (1.6)/(√(10)) = 0.506`

The standard error of the sulfate in a collection of 10 water samples is of 0.506 mg/L.