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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

Sagot :

Answer:

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

Step-by-step explanation:

Central Limit Theorem

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

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 [tex]\sigma = 1.6[/tex]

Collection of 10 samples:

This means that [tex]n = 10, s = \frac{1.6}{\sqrt{10}} = 0.506[/tex]

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

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