Chapter PVI, Problem 2RE

To determine

To explain is there any difference that the floral scent improved the subjects’ ability to complete the mazes.

Answer to Problem 2RE

Yes, there is difference that the floral scent improved the subjects’ ability to complete the mazes.

Explanation of Solution

It is given in the question that researchers want to find out can pleasant smells improve learning. Thus, the table is given which shows the time to complete the maze in seconds by unscented and scented ways. Thus, to find out is there any difference that the floral scent improved the subjects’ ability to complete the mazes we will use the calculator $\text{TI}-89$ . Thus, if the data are stored in two lists, say, $\text{list1 and list2}$ , create alist of the differences: Move the cursor to the name of an emptylist, 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- samplet -procedures, select $\text{2:T}-\text{Test or 2:}$ TIntervalfrom theSTATTests or Intsmenu. Specify as your data the list of differencesyou just created, and apply the procedure.So, we have,

Unscented	Scented	Difference
25.7	30.2	-4.5
41.9	56.7	-14.8
51.9	42.4	9.5
32.2	34.4	-2.2
64.7	44.8	19.9
31.4	42.9	-11.5
40.1	42.7	-2.6
43.2	24.8	18.4
33.9	25.1	8.8
40.4	59.2	-18.8
58	42.2	15.8
61.5	48.4	13.1
44.6	32	12.6
35.3	48.1	-12.8
37.2	33.7	3.5
39.4	42.6	-3.2
77.4	54.9	22.5
52.8	64.5	-11.7
63.6	43.1	20.5
56.6	52.8	3.8
58.9	44.3	14.6

And the hypothesis is defined as:

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

Thus, by using the calculator $\text{TI}-89$ , the test statistics and P-value come out to be:

  $\begin{array}{l}t=1.357\\ P=0.09494\end{array}$

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 there is difference that the floral scent improved the subjects’ ability to complete the mazes.