iPad 10:14 PM 93% Document HomeI Insert Draw Layout Review View Table Times New

ID: 3361129 • Letter: I

Question

iPad 10:14 PM 93% Document HomeI Insert Draw Layout Review View Table Times New Roma 10 A. #3 As a measure of impact of pollution along a river, the diversity of species along two (2) river floodplains (Vermillion River and the Black River) were studied. Randomly placed 50 x 20 meter plots were sampled along each river and the number of species of trees in each plot was recorded. The data are presented in the following table. Vermillion Black River River Identify the type of analysis to be carried out on these data. Explain. Formulate the appropriate hypotheses for these data (and explain your rational) List & discuss the appropriate evaluation and/or assumptions you will use for these data. Evaluate these assumptions using appropriate methods; present your results. Carry out the appropriate statistical procedures (alpha .05) and present your conclusions No If

Explanation / Answer

a)We need to test if there is any significant difference in the number of tree species between the two rivers. To do this, we need to carry out Two – sample t – test.

b) Here, our null hypothesis is -> H0 : mean difference = 0.
And our alternative hypothesis is -> H1 : mean difference 0.

c) Assumption is that the data from both the rivers follows normal distribution and the variance of the data of both the rivers are assumed to be equal.

d) For the second assumption, we use pooled variance.
For the first one, we plot the histogram of the data of both the rivers.

t-Test: Two-Sample Assuming Equal Variances

Vermillion river

Black river

Mean

11.15384615

9.444444444

Variance

5.641025641

16.02777778

Observations

Pooled Variance

9.795726496

Hypothesized Mean Difference

t Stat

1.25952676

P(T<=t) one-tail

0.111170578

t Critical one-tail

1.724718243

P(T<=t) two-tail

0.222341156

t Critical two-tail

2.085963447

Since p-value > 0.05, we accept the null hypothesis and conclude that there is no significant difference in the number of tree species near both the rivers.