Question

In order to simulate conditions near roads treated with road salt, scientists raised wood frog tadpoles in a high concentration of salt, and tadpole survival was measured. The survival rates for 5 replicates were 32, 37, 41, 45, and 50 percent. The sample mean for these values is 41 percent, and the sample variance is 48.5 percent squared. Determine the standard error of the sample mean for this data set.

Answer 1

Answer:

$SE_{\bar x} = 0.311$

Step-by-step explanation:

Given

$n=5$

$\bar x = 41\%$

$\sigma^2= 48.5\%$ --- variance

Required

The standard error of the sample mean

This is calculated as:

$SE_{\bar x} = \frac{\sigma}{\sqrt n}$

This can be rewritten as:

$SE_{\bar x} = \frac{\sqrt{\sigma^2}}{\sqrt n}$

So, we have:

$SE_{\bar x} = \frac{\sqrt{48.5\%}}{\sqrt 5}$

Rewrite as:

$SE_{\bar x} = \sqrt{\frac{48.5\%}{5}}$

$SE_{\bar x} = \sqrt{0.097}$

$SE_{\bar x} = 0.311$