Question

We measure the diameters for a random sample of 25 oak trees in a neighbourhood. Diameters of oak trees in the neighbourhood follow a normal distribution with standard deviation 8.25 cm. A confidence interval for the true mean diameter of all oak trees in the neighbourhood is calculated to be (36.191, 42.969). What is the confidence level of this interval

Answer 1

The required confidence inteval = 94.9%.

Explanation:

Confidence interval: Mean ± Margin of error

Given: A confidence interval for the true mean diameter of all oak trees in the neighbourhood is calculated to be (36.191, 42.969).

i.e. Mean + Margin of error = 42.969 (i)

Mean - Margin of error = 36.191 (ii)

Adding (i) and (ii), we get

`2Mean =79.16\\\\\Rightarrow\ Mean= 39.58`

Margin of error = 42.969-39.58 [from (i)]

= 3.389

Margin of error =
`t^* (\sigma)/(√(n))`

here n= 25
`, \ \sigma=8.25`

i.e.

`3.389=t^*(8.25)/(5)\\\\\Rightarrow\ t^* = (3.389)/(1.65)\\\\\Rightarrow\ t^* =2.0539 \`

Using excel function 1-TDIST.2T(2.054,24)

The required confidence inteval = 94.9%.