One of the most feared predators in the ocean is the great w

One of the most feared predators in the ocean is the great white shark. It is known that the white shark grows to a mean length of 19 feet; however, one marine biologist believes that great white sharks off the Bermuda coast grow much longer. To test this claim, full-grown white sharks were captured, measured, and then set free. However, this was a difficult, costly and very dangerous task, so only four sharks were actually sampled. Their lengths were 24, 25, 23,and 24 feet. Do the data provide sufficient evidence to support the claim? Use =0.01

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   19  
Ha:    u   >   19  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    3          
tcrit =    +   4.540702859      
              
Getting the test statistic, as              
              
X = sample mean =    24          
uo = hypothesized mean =    19          
n = sample size =    4          
s = standard deviation =    0.816496581          
              
Thus, t = (X - uo) * sqrt(n) / s =    12.24744871          
              
Also, the p value is              
              
p =    0.000586108          
              
Comparing |t| > 4.541, and P < 0.01, we   REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence that great white sharks off the Bermuda coast grow much longer than 19 feet. [CONCLUSION]