Chapter 25, Problem 26E

To determine

To explain is there evidence that the sexual images mattered.

Answer to Problem 26E

There is no sufficient evidence to support the claim that the sexual images mattered.

Explanation of Solution

The table of the advertisement remembered by the ways the images are shown is given in the question. It is also given that,

  $n=39$

And we will find the difference between the two samples as:

  

Now, the sample mean and the standard deviation of the difference are as follows:

  $\begin{array}{l}\overline{d}=\frac{0-1+\mathrm{....}-1+1}{39}\\ =0.2308\\ s_d=\sqrt{\frac{{(0-0.2308)}^2+{(-1-0.2308)}^2+\mathrm{....}+{(-1-0.2308)}^2+{(1-0.2308)}^2}{39-1}}\\ =1.6774\end{array}$

Let us now define the hypotheses as:

  $\begin{array}{l}{H}_0:{\mu }_d=0\\ H_a:{\mu }_d\ne 0\end{array}$

Now the degree of freedom is then as:

  $\begin{array}{l}df=n-1\\ =39-1\\ =38>35\end{array}$

Thus, the value of the test statistics is then as:

  $\begin{array}{l}t=\frac{\overline{d}}{s_d/\sqrt{n}}\\ =\frac{0.2308}{1.6774/\sqrt{39}}\\ =0.859\end{array}$

Thus, the P-value can be calculated using table T of appendix F as:

  $P>0.20$

As we know that the P-value is less than the significance level then the null hypothesis is rejected. Thus, we have,

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

Thus, we conclude that there is no sufficient evidence to support the claim that the sexual images mattered.