Question

You decide to study the effect of GRE preparatory course on GRE score. Describe, in detail, how you will design your study, how you will collect data, and how you are going to statistically test whether the GRE course had an effect on GRE score. Be as specific as you can about your hypotheses. How would you, if at all, change your study if you decided to study the effect of the GRE preparatory course on graduate school admission instead?

Answer 1

The GRE preparatory course and GRE score are dependent i.e GRE score may depend on GRE preparatory score.

To carry out the experiment I may collect the data from students of a particular university. The data may have columns whether the student has taken some GRE preparation course or not and corresponding GRE score.

Therefore now the data must be divided in two population say X and Y.

Let, Xbar= Arithmetic mean of sample of size n1 drawn from 1st population.

Ybar=Arithmetic mean of sample of size 21 drawn from 2nd population.

s^2=Mean square for pooled samples

Our hypothesis will be

H0: population mean for population are same

i.e. students taking GRE prepatory course and those not taking course have same mean.

VS

H1: population mean for population are not same

i.e. students taking GRE prepatory course and those not taking course do not have same mean.

Test statistic for the same will be

t = (Xbar-Ybar)/s*[(1/n1+1/n2)^0.5]

Thus, we reject H0 at level of significance if |t| >= t with (n1+n2-2) d.f. and (alpa/2) l.o.s. implying that population mean are not same i.e. GRE preparation course has no affect on GRE score.

Similarly if at all I wish to study the effect of the GRE preparatory course on graduate school admission then I will collect the data for students who took admission for graduation and ask whether they had taken any GRE preparation course.

Hypothesis may change to,

H0: same number of students who took GRE prepatory course and those not taking course have got admission.

VS

H1: Different number of students who took GRE prepatory course and those not taking course have got admission.

Rest of the testing procedur remain same.