a) To write an appropriate hypothesis. b) To explain do you think the assump

a) 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 perfomances of CPMP students with those taught using traditional curriculum. The data given in the question is:
$\begin{array}{|cccc|}\hline \text{Math Program}& n& Mean& SD\\ CPMP& 312& 29& 18.8\\ Traditional& 265& 38.4& 16.2\\ \hline\end{array}$
Thus, we define the hypotheses by:
${\displaystyle H_0:{\mu }_C={\mu }_T}$
${\displaystyle H_1:{\mu }_C\ne {\mu }_T}$
Where ${\displaystyle {\mu }_C=}$ The mean score of the core plus mathematics program (CPMP).
And ${\displaystyle {\mu }_T=}$ The mean score of the Traditional program.
b) 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 perfomances of CPMP students with those taught using traditional curriculum. The data given is:
$\begin{array}{|cccc|}\hline \text{Math Program}& n& Mean& SD\\ CPMP& 312& 29& 18.8\\ Traditional& 265& 38.4& 16.2\\ \hline\end{array}$
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)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 perfomances of CPMP students with those taught using traditional curriculum. The data given in the question is:
$\begin{array}{|cccc|}\hline \text{Math Program}& n& Mean& SD\\ CPMP& 312& 29& 18.8\\ Traditional& 265& 38.4& 16.2\\ \hline\end{array}$
Thus, the P-value given in the question is:
${\displaystyle P<0.0001}$
Therefore, the P-value means in this context that if means for the two programs are equal, there is a 1 in 1000 chance of seeing a difference as large as or larger than the observed difference just from natural sampling variation.
d) 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 perfomances of CPMP students with those taught using traditional curriculum. The data given in the question is:
$\begin{array}{|cccc|}\hline \text{Math Program}& n& Mean& SD\\ CPMP& 312& 29& 18.8\\ Traditional& 265& 38.4& 16.2\\ \hline\end{array}$
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.