Stats question help 912 Invasive Species In a study of the p

9.12 Invasive Species In a study of the pernicious giant hogweed, Jan Pergl^3 and associates compared the Density of these plants in two different sites within the Caucasus region of Russia. In its native area, the average density was found to be 5 plants/m^2. In an invaded area in the Czech Republic, a sample of n = 50 Plants produced an average density of 11.17 plants/m^2 With a standard deviation of 3.9 plants/m^2. a. Does the invaded area in the Czech Republic have an average density of giant hogweed that is different from mu = 5 at the a = 0.05 level of significance? What is the p-value associated with the test in part a? Can you reject at the 5% level of significance using the p-value?

Solution

Set Up Hypothesis
Null, it is same as 5, H0: U=5
Alternate, it is diffrent from 5, H1: U!=5
Test Statistic
Population Mean(U)=5
Sample X(Mean)=11.17
Standard Deviation(S.D)=3.9
Number (n)=50
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =11.17-5/(3.9/Sqrt(49))
to =11.187
| to | =11.187
Critical Value
The Value of |t | with n-1 = 49 d.f is 2.01
We got |to| =11.187 & | t | =2.01
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 11.1868 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho