91影视

We need to find convincing evidence of a linear relationship between $\mathrm{GPA}$and the number of pencils for students at this high school.

Consider:

$$\begin{gathered} \mathrm{n}=\mathrm{Sample}\mathrm{size}=\mathrm{Unknown} \\ \mathrm{伪}=\mathrm{Significance}\mathrm{level}=0.05 \end{gathered}$$

The estimate of the slope ${\mathrm{b}}_1$is given in the row "Pencils" and in the column "Coef" of the given computer output:

${\mathrm{b}}_1=-0.0423$

The estimated standard deviation of the slope ${\mathrm{SE}}_{\mathrm{b}1}$is given in the row "Time" and in the column "SE Coef" of the given computer output:

${\mathrm{SE}}_{\mathrm{b}1}=0.0631$

Given claim: Slope is nonzero (reduction):

The null hypothesis or the alternative hypothesis states the given claim The null hypothesis states that the slope is zero. If the given claim is the null hypothesis, then the alternative hypothesis states the opposite of the null hypothesis:

$$\begin{gathered} {\mathrm{H}}_0:{\mathrm{尾}}_1=0 \\ {\mathrm{H}}_{伪}:{\mathrm{尾}}_1<0 \end{gathered}$$

Compute the value of the test statistic

$\mathrm{t}=\frac{{\mathrm{b}}_1鈭�{\mathrm{尾}}_1}{{\mathrm{SE}}_{{\mathrm{b}}_1}}=\frac{鈭�0.0423鈭�0}{0.0631}鈮�鈭�0.6704$

The $\mathrm{P}$-Value is given in the row "Pencils" and in the column "P" of the computer output:

$\mathrm{P}=0.5062$