Chapter 10.2, Problem 54E

a.

To determine

To check: If sufficient evidences are provided by the data set that DDT affecting the mean height of the electrical response of second spike.

Answer to Problem 54E

Yes, data set is providing sufficient evidences.

Explanation of Solution

Given:

SAS output is:

  

Calculation:

The null and alternative hypotheses for the provided case are:

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_1:{\mu }_1\ne {\mu }_2\end{array}$

The test statistic is computed as:

  $\begin{array}{c}t=\frac{{\overline{x}}_1-{\overline{x}}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\\ =\frac{17.6-9.5}{\sqrt{\frac{{6.34}^2}{6}+\frac{{1.95}^2}{6}}}\\ =2.291\end{array}$

The degree of freedom is calculated as:

  $df=\min \left(n_1-1,n_2-1\right)=\min \left(6-1,6-1\right)=5$

The p-value:

  $P-value=0.0247$

In this case, $P-value=0.0247<0.05$

The null hypothesis could be rejected which is showing the sufficient evidences for the claim.

b.

To determine

To interpret: The P -value in the context of problem.

Explanation of Solution

The P -value is 0.0247 which implies that if all the means of population are same, the probability of having a sample mean difference or above is 0.0247.