Chapter 12, Problem 2CRE

To determine

To find: that these data provide compelling evidence of a straight-line relationship between thickness and gate speed of the populations of pistons from this metal alloy and conduct an effective X-level significance test.

Answer to Problem 2CRE

Yes

Explanation of Solution

Given:

  $\begin{array}{l}n=12\\ b=274.78\\ S{E}_b=88.18\end{array}$

Formula used:

  $t=\frac{b-{\beta }_0}{S{E}_b}$

Calculation:

The hypotheses:

  $\begin{array}{l}{H}_0:\beta =0\\ H_1:\beta \ne 0\end{array}$

The test statistic:

  $t=\frac{b-{\beta }_0}{S{E}_b}=\frac{274.78-0}{88.18}=3.116$

The P-value is the likelihood of the value or a more drastic result of the test. The P-value is the column title number (or interval) of Table B which contains the t-value in the row $df=n-2=12-2=10:$

  $0.005<P<0.01$

The null hypothesis is denied if the P-value is less than or equal to the significance-level:

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

There is enough proof to help the claim.