Question

Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence interval of left parenthesis 1.9 comma 3.3 right parenthesis when estimating the mean height​ (in centimeters) of a sample of seedlings. The estimated margin of error is nothing . The sample mean is nothing .

Answer 1

Answer:

$\bar X = \frac{Lower +Upper}{2}$

$\bar X= \frac{1.9+3.3}{2}= 2.6$

And the margin of error with this one:

$\bar X = \frac{Upper-Lower}{2}$

$ME = \frac{3.3-1.9}{2}= 0.7$

Step-by-step explanation:

Assuming that the parameter of interest is the sample mean $\mu$. And we can estimate this parameter with a confidence interval given by this formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)

For this case the confidence interval is given by (1.9, 3.3)

Since the confidence interval is symmetrical we can estimate the sample mean with this formula:

$\bar X = \frac{Lower +Upper}{2}$

$\bar X= \frac{1.9+3.3}{2}= 2.6$

And the margin of error with this one:

$\bar X = \frac{Upper-Lower}{2}$

$ME = \frac{3.3-1.9}{2}= 0.7$