Chapter PVI, Problem 33RE

(a)

To determine

To explain what role does randomization play in this experiment.

Explanation of Solution

It is given in the question that volunteer subjects are briefly shown seven cards, each displaying the name of a colour printed in a different colour. The subjects are asked to perform one or two tasks. Thus, the role randomization play in this experiment is that randomizing order of the tasks helps avoid the bias and memory effects. Also randomising the cards helps avoid bias as well.

(b)

To determine

To test appropriate hypotheses and state your conclusion.

Answer to Problem 33RE

The data do not provide evidence that the colour or written word dominates.

Explanation of Solution

It is given in the question that volunteer subjects are briefly shown seven cards, each displaying the name of a colour printed in a different colour. The subjects are asked to perform one or two tasks.Thus, to find out is there any difference we will use the calculator $\text{TI}-89$ . Thus, if the data are stored in two lists, say, $\text{list1 and list2}$ , create a list of the differences: Move the cursor to the name of an empty list, and then use VAR-LINK to enter the command $\text{list1}-\text{list2}$ . Press ENTER to perform the subtraction. Since inference for paired differences uses one-sample t -procedures, select $\text{2:T}-\text{Test or 2:}$ TIntervalfrom the STATTests or Intsmenu. Specify as your data the list of differences you just created, and apply the procedure. So, we have,

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

Thus, it is a two-tailed test and the list is as:

Subject	Colour	Word	Difference
1	4	7	-3
2	1	4	-3
3	5	6	-1
4	1	6	-5
5	6	4	2
6	4	5	-1
7	7	3	4
8	2	5	-3
9	7	5	2
10	4	3	1
11	2	0	2
12	5	4	1
13	6	7	-1
14	3	6	-3
15	4	6	-2
16	4	7	-3
17	4	3	1
18	7	4	3
19	4	3	1
20	0	6	-6
21	3	3	0
22	3	5	-2
23	7	3	4
24	3	7	-4
25	5	6	-1
26	3	4	-1
27	3	5	-2
28	1	4	-3
29	2	3	-1
30	5	3	2
31	3	4	-1
32	6	7	-1

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}P>0.05\\ t=-1.70\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

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

Thus, we conclude that the data do not provide evidence that the colour or written word dominates.