$1.$ Designing an Experiment $(5$ points$)$

Suppose we want to examine how different teaching methods and student educational backgrounds affect test

scores in a school. We have three teaching methods: Method A$,$ Method B$,$ and Method C$,$ and two backgrounds:

Preparatory and Public. We want to determine if there are any significant differences in test scores due to the

teaching methods and student educational backgrounds. You manage to get agreement from a high school

Principal to run a study on this topic.

You have three teachers, each of whom specializes in a given Method $($A$,$ B$,$ C$),$ each of whom will teach two

sections of the same class $-$ six in total $-$ in the upcoming Fall semester. For sake of argument, let$$s pretend they

are all teaching Statistics. The school takes feed$-$in students from several local preparatory schools, and from

several public $($primary$)$ schools. There are hundreds of candidates from each pool, and across the $180$ students

enrolled in the six sections of statistics, you want a balanced set of preparatory and public for each of the

Methods. Note that the two sections taught by the same teacher and Method can be merged $$ you don$$t need to

track this.

Write a one$-$to$-$two paragraph description of this $($do not copy$/$paste this provided question$),$ describe the

experiment you are running, design the experimental protocol and variable storage, and create the storage

data.frame, ready for grades to be input into the record column. Using the function head$(),$ display your resulting

data.frame as the final step of this problem