Question

Use the confidence interval to find the estimated margin of error. Then find the sample mean.

A biologist reports a confidence interval of (3.8,4.8 )when estimating the mean height​ (in centimeters) of a sample of seedlings.

Answer 1

Answer: The estimated margin of error = 0.5 centimeter

The sample mean = 4.3 centimeters

Explanation:

The confidence interval for population mean is given by :-

`\overline{x}\pm E`

or
`(\overline{x}-E,\ \overline{x}+E)`

, where
`\overline{x}` = sample mean.

E = Margin of error .

The given confidence interval : (3.8,4.8 )

Lower limit :
`\overline{x}-E=3.8` (1)

Upper limit =
`\overline{x}+E=4.8` (2)

Eliminate equation (1) from (2) , we get

`2E=1.0\\\\\Rightarrow\ E=(1)/(2)=0.5`

⇒ The estimated margin of error = 0.5 centimeter

Add (1) and (2) ,we get

`2\overline{x}-E=8.6\\\\\Rightarrow\ \overline{x}=(8.6)/(2)=4.3`

⇒ The sample mean = 4.3 centimeters