Question

A Nissan Motor Corporation advertisement read, “The average man’s I.Q. is $107.$ The average brown trout’s $I.Q.is4$. So why can’t man catch brown trout?” Suppose you believe that the brown trout’s mean I.Q. is greater than four. 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.

Short answer

p-value is $0.038$

Step-by-step solution

Given Information

We get the following information from the question itself:

Mean is $\frac{59}{12}=4.91667$

$s=1.62$

$$\begin{gathered} Ho:IQ<4 \\ Ha:IQ>4 \end{gathered}$$

$\alpha =0.05p$( reject $H_0$)

Explanation

To figure out,

Test statistics is $tdf=11=$$\frac{\overline{X}-mean}{{\displaystyle \frac{s}{\sqrt{n}}}}$

Critical value $t>1.796$

Calculation:

$t=\frac{0.916667}{{\displaystyle \frac{1.62}{\sqrt{12}}}}=1.96$

reject $H_0$and $IQ>4$

$p$value is $0.038$