Chapter PVI, Problem 26RE

(a)

To determine

To explain were the two forms (A/B) of the test equivalent terms of difficulty and test an appropriate hypothesis and state your conclusion.

Answer to Problem 26RE

There is sufficient evidence that the two forms (A/B) of the test are equivalent terms of difficulty.

Explanation of Solution

It is given in the question that the educational testing service is now administering several of its standardized tests online-the CLEP and GMAT exams, for example. 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,

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

It is a two-tailed test and the list is as follows:

Subject	Test A	Test B	Difference
1	14	13	1
2	10	13	-3
3	16	8	8
4	15	14	1
5	17	16	1
6	14	11	3
7	9	12	-3
8	12	12	0
9	16	16	0
10	7	14	-7
11	13	8	5
12	13	11	2
13	17	15	2
14	13	11	2
15	14	13	1
16	9	9	0
17	9	15	-6
18	15	14	1
19	12	16	-4
20	10	8	2

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

  $\begin{array}{l}P=0.7078\\ t=0.38\end{array}$

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 sufficient evidence that the two forms (A/B) of the test are equivalent terms of difficulty.

(b)

To determine

To explain is there evidence that the testing environment (paper/online) matters and test an appropriate hypothesis and state your conclusion.

Answer to Problem 26RE

There is insufficient evidence that the testing environment (paper/online) matters.

Explanation of Solution

It is given in the question that the educational testing service is now administering several of its standardized tests online-the CLEP and GMAT exams, for example.Thus, for testing the hypothesis we will use the calculator $\text{TI}-89$ as, first we will go in the STAT TESTS menu, choose $4:2-$ SampTTest. Then you must specify if you are using data stored in two lists or if you will enter the means, standard deviations, and sizes of both samples. You must also indicate whether to pool the variances (when in doubt, say no) and specify whether the test is to be two-tail, lower-tail, or upper-tail. So, now we will define the hypothesis as:

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

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

  $\begin{array}{l}P=0.8236\\ t=-0.22\end{array}$

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 thatthere is insufficient evidence that the testing environment (paper/online) matters.