Chapter 27, Problem 27E

a)

To determine

To state the hypotheses about the slope.

Answer to Problem 27E

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

Explanation of Solution

Given:

  

The null and alternative hypotheses:

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

That means,

  $H_0:$ There is no association between pH and BCI.

  $H_a:$ There is an association between pH and BCI.

b)

To determine

To perform the hypothesis test.

Answer to Problem 27E

t = -7.731 and p-value = 0

Explanation of Solution

Given:

  

Formula:

Test statistic:

  $t=\frac{b-{\beta }_0}{S{E}_b}$

Test statistic:

  $t=\frac{-197.694-0}{25.57}=-7.731$

The degrees of freedom = df = 161

Therefore, p-value would be,

P-value = 0 …Using excel formula, =TDIST(6.9674,26,2)

c)

To determine

To state a conclusion.

Answer to Problem 27E

There is sufficient evidence that the slope is non zero and there is association between pH and BCI.

Explanation of Solution

Given:

  

Decision: P-value < 0.05, reject H₀.

Conclusion: There is sufficient evidence that the slope is non zero and there is association between pH and BCI.