The changing ecology of the swamps in Louisiana has been the

The changing ecology of the swamps in Louisiana has been the subject of much environmental research. One water-quality parameter of concern is the total phosphorous level. Suppose that the EPA makes 15 measurements in one area of the swamp, yielding a mean level of total phosphorus of 12.3 parts per billion (ppb) and a standard deviation of 5.4 ppb. The EPA wants to test whether the data support the conclusion that the mean level is less than 15 ppb. How much evidence do we have that the mean level of phosphorus is less than 15 parts per billion?

A. No evidence

B. Some evidence

C. Strong evidence

D. Very strong evidence

E. Extremely strong evidence

Solution

Formulating the null and alternative hypotheses,          
          
Ho:   u   =   15
Ha:    u   =/=   15
          
As we can see, this is a    1   tailed test.  
          
          
Getting the test statistic, as          
          
X = sample mean =    12.3      
uo = hypothesized mean =    15      
n = sample size =    15      
s = standard deviation =    5.4      
          
Thus, t = (X - uo) * sqrt(n) / s =    -1.936491673      
          
Also, the p value is          
          
p =    0.036629222      
          

Please refer to the convention in your class as to in which category this one falls. It seems your class agreed to some standard.