Refer to Exercise 12.S.2. Consider the null hypothesis that sulfur dioxide concentration has no effect on yield.
(a) Assuming that the linear model holds, formulate this as a hypothesis about the true regression line.
(b) Write a directional alternative, in symbols, that says increasing sulfur dioxide tends to decrease yield.
(c) How many degrees of freedom are there for the test that compares the hypotheses in (a) and (b)?
(d) The sample slope, b1, is -2.262 and the standard error of the slope is 0.4421. Compute the value of the test statistic.
(e) The P-value for the test is 0.0002. [f a = 0.05, state your conclusion regarding the null hypothesis in the context of this setting.