Chapter 27, Problem 29E

a)

To determine

To test an appropriate hypothesis.

Answer to Problem 29E

There is sufficient evidence that the slope is non zero and the relationship is significant.

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:

  $t=\frac{6.650-0}{1.910}=3.482$

The degrees of freedom = df = 14

Therefore, p-value would be,

P-value = 0.0037 …Using excel formula, =TDIST(3.482,14,2)

Decision: P-value < 0.05, reject H₀.

Conclusion: There is sufficient evidence that the slope is non zero and the relationship is significant.

b)

To determine

To explain whether the population of a city is a useful predictor of ozone level.

Answer to Problem 29E

The population of city is useful predictor.

Explanation of Solution

Given:

  

The R-square = 84.4% which is high. Therefore, the population of city is useful predictor.