Chapter 12.1, Problem 2.1CYU

To determine

To explain do these data provide convincing evidence of a linear relationship between pack weight and body weight in the population of the ninth-grade students at the school and carry out an appropriate test at the $\alpha =0.05$ level.

Answer to Problem 2.1CYU

There is sufficient evidence to support the claim of a linear relationship between pack weight and body weight in the population of the ninth-grade students at the school.

Explanation of Solution

It is given in output that:

  $\begin{array}{l}n=8\\ b=0.09080\\ {\text{SE}}_b=0.02831\end{array}$

Thus, we define the hypothesis by:

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

Thus, the value of the test statistics is as:

  $\begin{array}{l}t=\frac{b-\beta }{{\text{SE}}_b}\\ =\frac{0.09080-0}{0.02831}\\ =3.2073\end{array}$

And the degrees of freedom is:

  $\begin{array}{l}df=n-2\\ =8-2\\ =6\end{array}$

Thus, the P-value is as:

  $0.006<P<0.018$

As we know that if the P-value is less than or equal to the significance level, then the null hypothesis is rejected as:

  $P<0.05\Rightarrow \text{ Reject }{H}_0$

Thus, we conclude that there is sufficient evidence of a linear relationship between pack weight and body weight in the population of the ninth-grade students at the school.