Question: 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 not less than or equal to four. You catch some brown trout. A fish psychologist determines the I.Q.s of the caught brown trout as follows: 3; 6; 7; 3; 6; 4; 5; 3; 6; 5; 4; 5. The standard deviation of the I.Q.s listed is approximately 1.36. Conduct a hypothesis test of your belief:
(a) Use a significant level of 4.5% and showing your complete work, write down your conclusion as a complete sentence.
(b) What would be the conclusion if you used a significant level of 1%? In sentence form a conclusion in a complete sentence.