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:

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%.

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