Chapter 24, Problem 9E

(a)

To determine

To write an appropriate hypothesis.

Answer to Problem 9E

  $\begin{array}{l}{H}_0:{\mu }_C={\mu }_T\\ H_1:{\mu }_C\ne {\mu }_T\end{array}$

Explanation of Solution

The core plus mathematics program (CPMP) is an innovative approach to teaching mathematics. After field test in high schools over a three-year period, researchers compared the performances of CPMP students with those taught using traditional curriculum. The data given in the question is:

Math Program	n	Mean	SD
CPMP	312	29	18.8
Traditional	265	38.4	16.2

Thus, we define the hypotheses by:

  $\begin{array}{l}{H}_0:{\mu }_C={\mu }_T\\ H_1:{\mu }_C\ne {\mu }_T\end{array}$

Where ${\mu }_C=$ The mean score of the core plus mathematics program (CPMP).

And ${\mu }_T=$ The mean score of the Traditional program.

(b)

To determine

To explain do you think the assumptions for inference are satisfied.

Answer to Problem 9E

Yes, it is satisfied.

Explanation of Solution

The core plus mathematics program (CPMP) is an innovative approach to teaching mathematics. After field test in high schools over a three-year period, researchers compared the performances of CPMP students with those taught using traditional curriculum. The data given in the question is:

Math Program	n	Mean	SD
CPMP	312	29	18.8
Traditional	265	38.4	16.2

Thus, the assumptions for inference are satisfied because the groups are independent. Though, we do not know if students were randomly assigned to the program so we are assuming that they are randomly assigned. And the samples sizes of both the groups: CPMP and Traditional program are large so the central limit theorem applies and so does the normal condition. Thus, the conditions are satisfied.

(c)

To determine

To explain what the P-value means in this context.

Explanation of Solution

The core plus mathematics program (CPMP) is an innovative approach to teaching mathematics. After field test in high schools over a three-year period, researchers compared the performances of CPMP students with those taught using traditional curriculum. The data given in the question is:

Math Program	n	Mean	SD
CPMP	312	29	18.8
Traditional	265	38.4	16.2

Thus, the P-value given in the question is:

  $P<0.0001$

Therefore, the P-value means in this context that if means for the two programs are equal, there is a $1\text{ in 1000}$ chance of seeing a difference as large as or larger than the observed difference just from natural sampling variation.

(d)

To determine

To state a conclusion about the CPMP program.

Explanation of Solution

The core plus mathematics program (CPMP) is an innovative approach to teaching mathematics. After field test in high schools over a three-year period, researchers compared the performances of CPMP students with those taught using traditional curriculum. The data given in the question is:

Math Program	n	Mean	SD
CPMP	312	29	18.8
Traditional	265	38.4	16.2

Thus, the conclusion about CPMP is that on average, students who learn with the CPMP method do significantly worse on Algebra tests that do not allow them to use calculators than the students who learn by traditional methods.