Chapter 27, Problem 30E

a)

To determine

To test an appropriate hypothesis.

Answer to Problem 30E

There is sufficient evidence that the slope is non zero and there is a significant association between sales and profits.

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:

  $t=\frac{0.092498-0}{0.0075}=12.333$

The degrees of freedom = df = 77

Therefore, p-value would be,

P-value = 0 …Using excel formula, =TDIST(12.333,77,2)

Decision: P-value < 0.05, reject H₀.

Conclusion: There is sufficient evidence that the slope is non zero and there is a significant association between sales and profits.

b)

To determine

To explain whether the company’s sales serve as a useful predictor of its profits.

Answer to Problem 30E

The company’s serve as useful predictor of its profits.

Explanation of Solution

Given:

  

The R-square = 66.2% which is moderately high and standard deviation is 466.2 which is much higher than standard error of coefficient. Therefore, the company’s serve as useful predictor of its profits.