Determine what the original populations might have been in each town. Show your thinking. a) The population of Town A increased by 10%.
The population of Town B decreased by 5%.
Now the populations of the two towns are the same.

[0.841;6.879]

Step-by-step explanation:

Hello!

You have two independent samples:

Sample 1

X₁: tree species in an unlogged plot.

n₁= 12 plots

Unlogged 22 18 22 20 15 21 13 13 19 13 19 15

Sample 2

X₂: tree species in a plot logged 8 years earlier

n₂= 9

Logged 17 4 18 14 18 15 15 10 12

The objective of this experiment is to estimate the difference between the means of the number of species on the unlogged plots and the logged plots. Symbolically: μ₁-μ₂

To be able to estimate the difference between the two population means, I'll assume that both variables have a normal distribution and use a pooled t-statistic for the Confidence interval. (I did a quick F-test for variance homogeneity, population variances are unknown but equal)

The formula is:

(X₁[bar]-X₂[bar])±*(Sₐ√(1/n₁+1/n₂))

Where

sample mean sample 1 X₁[bar]= 17.50

sample mean sample 2 X₂[bar]= 13.64

S₁= 3.53

S₂= 4.50

Sₐ²= (n₁ - 1)S₁² + (n₂ - 1)S₂² = 11*(3.53)² + 8*(4.50)² = 15.74

                   n₁+n₂-2                            19

Sₐ= 3.96

Now replace the values in the formula:

(X₁[bar]-X₂[bar])±*(Sₐ√1/n₁+1/n₂)

[(17.50-13.64) ± 1.729*(3.96*√(1/12+1/9))]

[3.86 ± 3.019]

[0.841;6.879]

With a confidence level of 90%, you'd expect that the interval [0.841;6.879] contains the difference between the means of the number of species on the unlogged plots and the logged plots.

I hope it helps!