Question

Your body loses sodium when you sweat. Researchers sampled 38 random tennis players. The average sodium loss was 500 milligrams per pound and the standard deviation was 62 milligrams per pound. Construct and interpret a 99% confidence interval to estimate the mean loss in sodium in the population.

Answer 1

Answer:

The 99% confidence interval to estimate the mean loss in sodium in the population is between 474.10 milligrams and 525.90 milligrams. This means that we are 99% that the true mean loss in sodium in the population is between 474.10 milligrams and 525.90 milligrams.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.99}{2} = 0.005$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.005 = 0.995$, so $z = 2.575$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.575*\frac{62}{\sqrt{38}} = 25.90$

The lower end of the interval is the mean subtracted by M. So it is 500 - 25.90 = 474.10 milligrams.

The upper end of the interval is the mean added to M. So it is 500 + 25.90 = 525.90 milligrams

The 99% confidence interval to estimate the mean loss in sodium in the population is between 474.10 milligrams and 525.90 milligrams. This means that we are 99% that the true mean loss in sodium in the population is between 474.10 milligrams and 525.90 milligrams.