Suppose I was a teacher who had recently introduced a new way to teach young chi

Question

Suppose I was a teacher who had recently introduced a new way to teach young children to learn math. I have a group of 6 year olds that I have taught with my new method. I have tested the math skills of my group and I wish to compare the math skills of my class to those of the general population of 6 year olds. How will the Sampling Distribution of the mean help me to determine if my group has higher math skills than the general population? Why is the Sampling Distribution of the mean important for this task?

Explanation / Answer

We have a group of students of age 6 whom the teacher taught with new math skills. And now we have another group of students of age 6 who were taught with conventional methods. We assume that the merit and background of the students in both the groups are equal on an average( i.e, the students under new teaching methods are on an average of similar intellectual faculty and merit with the group under conventional method)

Now to compare the skills a test can be conducted on math with the same set of question and test scores are recorded for each group and then their means are compared if the means are "significantly" differing from each other that is if the first group has smaller mean then the new method has adverse effect and if greater then the new method improves upon the previous teaching.

Differing from each other "significantly" means we have to carry out a two-sample t-test with the with NULL hypothesis as that the two means are equal and alternative being they are different.

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