Chapter 12.1, Problem 15E

To determine

To find: that these data is providing convincing evidence at the $\alpha \text{=0}\text{.05}$ .

Answer to Problem 15E

There is enough convincing proof that more lamb’s quarts reduce corn yield.

Explanation of Solution

Given:

  

  $\begin{array}{l}n=\text{16}\\ \alpha \text{=Significance level =0}\text{.05}\end{array}$

Given claim: Slope is negative (reduction)

Calculation:

The calculation of the slope $b_1$ is mention in the row “Weeds per meter” and in the column “Coef” of the mention computer output:

  $b_1=-1.0987$

The calculated standard deviation of the slope $S{E}_{b_1}$ is mention in the row “Weeds per meter” and in the column “SE Coef” of the mention computer output:

  $S{E}_{b_1}=0.5712$

The null hypothesis or the alternative hypothesis is the statement the mention claim. The null hypothesis is the statements that slope is zero. If the given claim is the null hypothesis, then the alternative hypothesis statement is the opposite of the null hypothesis.

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_0:{\beta }_1<0\end{array}$

The P-value is the probability of getting the value of the statistic, or a value more extreme. $df-n-2=16-2=14$

  $0.025<P<0.05$

If the P-value is equal or lesser than to the significance level, then the null hypothesis is rejected:

  $P<0.05\Rightarrow \text{Reject }{H}_0$

There is enough convincing proof that more lamb’s quarts reduce corn yield.