Answer:
The required confidence inteval = 94.9%.
Step-by-step 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
[tex]2Mean =79.16\\\\\Rightarrow\ Mean= 39.58[/tex]
Margin of error = 42.969-39.58 [from (i)]
= 3.389
Margin of error = [tex]t^* \dfrac{\sigma}{\sqrt{n}}[/tex]
here n= 25 [tex], \ \sigma=8.25[/tex]
i.e.
[tex]3.389=t^*\dfrac{8.25}{5}\\\\\Rightarrow\ t^* = \dfrac{3.389}{1.65}\\\\\Rightarrow\ t^* =2.0539 \[/tex]
Using excel function 1-TDIST.2T(2.054,24)
The required confidence inteval = 94.9%.
