Conservationists have despaired over destruction of tropical rain forest by logging, clearing, and burning." These words begin a report on a statistical study of the effects of logging in Borneo. Here are data on the number of tree species in 12 unlogged forest plots and 9 similar plots logged 8 years earlier: Col1 Unlogged 2218 222015121 13 13 1913 19 15

Col2 Logged 17 4 181418151510 12 Use the data to give a 90% confidence interval for the difference in mean number of species between unlogged and logged plots. Compute degrees of freedom using the conservative methoo. Interval: to.

-8.16 to 15.84

Step-by-step explanation: Confidence Interval is an interval in which we are a percentage sure the true mean is in the interval.

A confidence interval for a difference between two means and since sample 1 and sample 2 are under 30, will be

±

where

x₁ and x₂ are sample means

t is t-score

is estimate of standard deviation

n₁ and n₂ are the sample numbers

The estimate of standard deviation is calculated as

where

s₁ and s₂ are sample standard deviation of each sample

Degrees of freedom is:

df = 12 + 9 - 2

df = 19

Checking t-table, with 90% Confidence Interval and df = 19, t = 1.729.

The mean and standard deviation for 12 unlogged forest plots are 17.5 and 3.53, respectively.

The mean and standard deviation for 9 logged plots are 13.66 and 4.5, respectively.

Calculating estimate of standard deviaton:

15.74

The difference between means is

= 17.5 - 13.66 = 3.84

Calculating the interval:

=

=

=

= 12

Then, interval for the difference in mean is 3.84 ± 12, which means the interval is between:

lower limit: 3.84 - 12 = -8.16

upper limit: 3.84 + 12 = 15.84

The interval is from -8.16 to 15.84.