Chapter 24, Problem 23E

(a)

To determine

To explain do these results indicate that the viewer memory for ads may differ depending on program content and state your conclusion.

Answer to Problem 23E

This does not indicate that the viewer memory for ads may differ depending on program content.

Explanation of Solution

It is given in the question that a test of the hypothesis that there is no difference in ad memory between programs with sexual content and those with violent content has a P-value of $0.136$ . Thus, we know that if the P-value is smaller than the significance level then the null hypothesis is rejected. So,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, this conclude that there is no sufficient evidence to support the claim of a difference. Therefore, this does not indicate that the viewer memory for ads may differ depending on program content.

(b)

To determine

To explain is there any evidence that the viewer memory for ads may differ depending on program content.

Answer to Problem 23E

Yes, there is evidence that the viewer memory for ads may differ depending on program content.

Explanation of Solution

It is given that:

  $\begin{array}{l}{\overline{x}}_1=1.71\\ {\overline{x}}_2=3.17\\ n_1=108\\ n_2=108\\ s_1=1.76\\ s_2=1.77\end{array}$

Now, let us define the hypotheses:

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

Thus, the value of test statistics is:

  $\begin{array}{l}t=\frac{{\overline{x}}_1-{\overline{x}}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\\ =\frac{1.71-3.17}{\sqrt{\frac{{1.76}^2}{108}+\frac{{1.77}^2}{108}}}\\ =-6.08\end{array}$

And the degree of freedom is as:

  $\begin{array}{l}df=\frac{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2})}{\frac{{(\raisebox{1ex}{$s_1^2$}\!\left/ \!\raisebox{-1ex}{$n_1$}\right.)}^2}{n_1-1}+\frac{{(\raisebox{1ex}{$s_2^2$}\!\left/ \!\raisebox{-1ex}{$n_2$}\right.)}^2}{n_2-1}}\\ =214\end{array}$

Thus, the P-value will be as:

  $P<0.01$

And as we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected. So,

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

Thus, we conclude that there is sufficient evidence to support the claim. So, there is evidence that the viewer memory for ads may differ depending on program content.