   SEARCH HOME Math Central Quandaries & Queries  Question from Lin:

PLEASE HELP WITH THIS VERY DIFFICULT STATISTICS QUESTION(the process would really help)
Imagine you and your 4 study group partners are interested in whether all
those hours you spent together working on statistics problems for midterm
exam 2 actually helped your group's performance on that exam relative to its
performance on the first midterm exam. Suppose the first and second midterm
grades were as follows:
Is there sufficient evidence (at a = :05) to conclude that the group performed
better on midterm 2? Please provide all your calculations.

midterm 1 midterm 2
A 25 28
B 20 19
C 15 21
D 16 25
E 20 22 Hi Lin,

Is this really the way the problem was worded? Can you conclude that the group performed better on the second test? Of course they did. Four of the five students improved their grades and the average improvement was 3.8 points. You don’t need any statistics to see this, you just have to do the arithmetic. The problem should be worded something like this.

A teacher wanted to see if studying together improves the grades on statistics midterms. To do this she randomly selected 5 students who studied alone and recorded their grades on the first midterm. She then had them study together for the second midterm and recorded their grades. From the results is their sufficient evidence (at $\alpha = 0.0.$) to conclude that studying together improves performance?

Let $X$ be the random variable that is the score on the first midterm, $Y$ be the random variable that is the score on the second midterm and $d = Y – X.$ Let $\mu_X$ be the mean score on the first midterm for students who studied alone, $\mu_Y$ be the mean score on the second midterm for students who studied together and $\mu_d = \mu_Y - \mu_{X}.$ Use the data below to test the hypothesis that $\mu_d = 0$ against the alternate hypothesis that $\mu_d > 0.$

X Y d
A 25 28 3
B 20 19 -1
C 15 21 6
D 16 25 9
E 20 22 2

This is now a one sample t-test rather than a two sample test.

Can you complete the problem now? Write back if you need more assistance,
Penny       * Registered trade mark of Imperial Oil Limited. Used under license. Math Central is supported by the University of Regina and the Imperial Oil Foundation.