Question

A test of abstract reasoning is given to a sample of students before and after they completed a formal logic course. Assume that two dependent samples have been randomly selected from normally distributed populations. The results are given below. At the 0.05 significance level, use critical value method to test the claim that the mean score is not affected by the course. Does the course improve the students’ skill on abstract reasoning?

     Before 74 83 75 88 84 63 93 84 91 77

     After 73 77 70 77 74 67 95 83 84 75

1. State the requirement
2. State the null and alternative hypotheses with the correct symbols
3. Write all the statistics
4. Write the formula of the test statistic and find the test statistic (you may use a calculator, but you are required to write down the command and all the numbers you enter)
5. Find the critical value or the P-value (you may use a calculator, but you are required to write down the command and all the numbers you enter)
6. Decide to reject or fail to reject H₀ and explain the reason
7. Wording the conclusion
8. Answer the question based on your result above

Answer 1

Let be the population means of score of before and after taking the course respectively .

Hypothesis :

or simply :

where ,

Test statistic :

where

We make the following table and calculate the above statistics :

and  

So, test stsatistic :

This is a twotailed test . So p value is given by :

P[t9 >2364] = 0.0212

So,

Note that p value <alpha= 0.05   

So we have enough evidence to reject the null hypothgesis .

Or in simpler words , The course has actually affected the scores .