Chapter 27, Problem 24E

a)

To determine

To test an appropriate hypothesis about the association between brain size and IQ.

Answer to Problem 24E

There is not sufficient evidence that the slope is non zero and there is no association between the Size and the IQ-Verbal.

Explanation of Solution

Given:

  

Formula:

Test statistic:

  $t=\frac{b-{\beta }_0}{S{E}_b}$

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

Test statistic:

  $t=\frac{0.098842-0}{0.0884}=1.118$

The degrees of freedom = df = 18

Therefore, p-value would be,

P-value = 0.2783 …Using excel formula, =TDIST(1.118,18,2)

Decision: P-value > 0.05, fail to reject H₀.

Conclusion: There is not sufficient evidence that the slope is non zero and there is no association between the Size and the IQ-Verbal.

b)

To determine

To state a conclusion about the strength of an association.

Answer to Problem 24E

The strength of the association is very weak.

Explanation of Solution

Given:

  

The R-square = 6.5% which is very less. Therefore, the strength of the association is very weak.