Question

Scientists at the Hopkins Memorial Forest have been collecting environmental data for more than 100 years. Sulfate content in water samples from Birch Brook is known to be 7.38mg/L with a standard deviation of 1.60mg/L. If 10 students measure the sulfate in their samples to together estimate the mean, what is the probability that they get a sampling error of greater than 1.0 mg/L? What assumptions do we need to make to calculate that value?

Answer 1

Answer:

The probability that they get a sampling error of greater than 1.0 mg/L is 0.04.

To calculate this value, I assume that the samples are randomly collected

Step-by-step explanation:

Sampling error can be calculated using the formula

$\frac{t*s}{\sqrt{n}}$  where

• t is the statistic of the probability getting the standard error

• s is the standard deviation (1.60mg/L)

• n is the sample size (10)

For the sampling error of 1.0mg/L we have

$1=\frac{t*1.60}{\sqrt{10}}$    

Solving for t we have t≈1.976

Then the probability that they get a sampling error of greater than 1.0 mg/L is

P(t>1.976) ≈ 0.04.

In other words, we are 96% confident that the sampling error is within 1.0 mg/L.

To calculate this value, I assume that the samples are randomly collected.