A Nissan Motor Corporation advertisement read The average ma

A Nissan Motor Corporation advertisement read, “The average man’s I.Q. is 107. The average brown trout’s I.Q. is 4. So why can’t man catch brown trout?” Suppose you believe that the brown trout’s mean I.Q. is greater than 4. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief. Use a significafcant level of 5%. Standard Deviation of the I.Q listed is 1.62.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   4  
Ha:    u   >   4  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    11          
tcrit =    +   1.795884819      
              
Getting the test statistic, as              
              
X = sample mean =    4.916666667          
uo = hypothesized mean =    4          
n = sample size =    12          
s = standard deviation =    1.621353718          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.958503222          
              
Also, the p value is              
              
p =    0.038004087          
              
Comparing t > 1.796 (or, p <0.05), we   REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence that the brown trout’s mean I.Q. is greater than 4. [CONCLUSION]