The destruction of the tropical rain forest due to logging, clearing and burning
ID: 3041145 • Letter: T
Question
The destruction of the tropical rain forest due to logging, clearing and burning is a major concern
for conservationists around the world. Data were collected on number of tree species in 31 plots that were not
logged and 29 plots that had been logged 8 years earlier. Researchers would like to estimate the difference in
the average number of tree species between the logged and unlogged rain forest plots and test to see if the
difference is significant. The populations are assumed to be normally distributed. Use a significance level of
0.05.
a. Explore: Interpret the side by side boxplot. Include statements about the shape center and spread
of each group. Include context.
b. State: What is the question of interest?
c. Plan: State the null and alternative hypotheses.
d. Solve: Check the conditions for inference.
e. Solve: Calculate the test statistic. Show work!
f. Solve: State the degrees of freedom.
g. Solve: Give the appropriate p-value and state whether it is one-sided or two-sided.
h. Solve: Calculate the appropriate 95% confidence interval. Show work!
i. Conclude: Finally, using the results from parts g and h, summarize your conclusions. Interpret the
CI and results of your test. Use the four part conclusion method.
ST 202: Activity 2 Submit only pages from this section. Add more pa 40 Points Name: Q1. (17 points) The destruction of the tropical rain fo for conservationists around the world. Data were cc logged and 29 plots that had been logged 8 years e the average number of tree species between the la difference is significant. The populations are assun 0.05. Number of tree species per rain forest plot in Borneo: Logged vs Unlogged logged unlogged 1214 1618 20 22 a. Explore: (2 pts) Interpret the side by side bor of each group. Include context. b. State: (lpt) What is the question of interest? e Plan: (2nts). State the mlland alternative hvnExplanation / Answer
(a and b)
Min. 1st Qu. Median Mean 3rd Qu. Max.
4.00 12.00 15.00 13.67 17.00 18.00
[1] 4.5
[1] 9
Min. 1st Qu. Median Mean 3rd Qu. Max.
13.00 14.00 18.00 17.36 20.50 22.00
[1] 3.668044
[1] 11
(c)
No, there is no visual evidence that the average number of species of trees in the logged plots is different than the unlogged plots because two plots are overlap
(d)
Null hypothesis: The difference is not significant
Alternative hypothesis: The difference is significant
(e) The output of R code is below.
Welch Two Sample t-test
data: logged and unlogged
t = -1.9837, df = 15.417, p-value = 0.06539
alternative hypothesis: true difference in means is not equal to 0
90 percent confidence interval:
-6.9582227 -0.4357167
sample estimates:
mean of x mean of y
13.66667 17.36364
The test statistic is
t= -1.9837
The degree of freedom = n1+n2-2=18
(f) The p-value =2*P(t <-1.9837 with df=n1+n2-2=18) =0.0628 (from student t table)
(g) Given a=0.1, t(0.05, df=11+9-2=18) =1.73 (from student table)
So 90% confidece interval is
(xbar1-xbar2) +/- t*sqrt(s1^2/n1+s2^2/n2)
--> (13.67-17.36) +/- 1.73*sqrt(4.5^2/9+3.668044^2/11)
--> (-6.914091, -0.465909)
(h)p-value = 0.06539
Yes, my answers are different
(i) Based on the box-plot, we can not conclude that there is a signifcant different between the logged an unlogged rain forest.
Since the p-value is larger than significant level 0.05 (two-sided test), we do not reject the null hypothesis. Based on the analysis, we can not conclude that there is a significant difference between the logged and unlogged rain forest plots.
However, the researchers can estimate the difference in the average number of tree species between the logged and unlogged rain forest plots.