Chapter 27, Problem 7E

a)

To determine

To state the hypotheses about the slope.

Answer to Problem 7E

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

Explanation of Solution

Given:

  

The null and alternative hypotheses:

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

b)

To determine

To perform the hypothesis test.

Answer to Problem 7E

There is sufficient evidence that the slope is non zero and there is association between Calories and Sodium intake.

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:

  $t=\frac{2.29959-0}{0.5607}=4.101$

The degrees of freedom = df = 11

Therefore, p-value would be,

P-value = 0.0018 …Using excel formula, =TDIST(4.101,11,2)

Decision: P-value < 0.05, reject H₀.

Conclusion: There is sufficient evidence that the slope is non zero and there is association between Calories and Sodium intake.