Question

A group of prospective graduate students seeking an MBA take a GMAT preparation class in hope of increasing their score on this important test. On the first night of class, before any instruction is given, a sample GMAT is given, and the scores are recorded. On the last night of class, another sample GMAT is given, and once again the scores are recorded. At the five percent level of significance, can you conclude that the instruction was effective in increasing GMAT scores?

Data is as follows

Before 596 401 378 457 518 339 404 482 433 347 433 460 355 459 370

After 421 543 493 496 614 547 438 561 502 613 474 535 347 319 487

Answer 1

Here, there are two groups of data. Let us denote before instruction data be X & After instruction data be Y. i.e.

X= 596 401 378 457 518 339 404 482 433 347 433 460 355 459 370
Y= 421 543 493 496 614 547 438 561 502 613 474 535 347 319 487

We have to test that instruction was effective in increasing in GMAT Score. This can be tested by t-test.

H0: there is no effect instruction means the mean of GMAT score before instruction is same as after instruction.

H1: There is the effect of instruction

as the sample size is 15 (less than 30). So, we can use 2 sample t-test.

calculate the mean of both group

mean(X)= 428.8 & mean(Y)= 492.6667 & d.f= 15+15-2=28

Tabulated value of t at 28 d.f. is 2.05.

Since tcal>tcal. So, we can reject the null hypothesis means there is an effect of instructions on GMAT Score.