Question 1203947
i believe this will require the use of a two sample paired t-test.


you find the differnces in the score of sample 2 minus sample 1 results for each student that participated.


i used the calculator at <a href = "https://www.mathportal.org/calculators/statistics-calculator/t-test-calculator.php" target = "_blank">https://www.mathportal.org/calculators/statistics-calculator/t-test-calculator.php</a>


here are the results.


<img src = "http://theo.x10hosting.com/2023/092911.jpg">


<img src = "http://theo.x10hosting.com/2023/092912.jpg">


<img src = "http://theo.x10hosting.com/2023/092913.jpg">


<img src = "http://theo.x10hosting.com/2023/092914.jpg">


the procedures is to find the differences for each pair.
then find the mean and the standard deviation of the distiribution of paired differnces.
then calculate the standard error = standard deviation divided by square root of sample size.
then do the t-test.
then check the test t-score against the critical t-score.
if it's greater, then the test results are significant and you conclude thre's a diference.
if not, then you conclude that there is no difference.



the results of this test indicate that the results are not significant because the test t-score was less than the critical t-score.


the conclusion is that the tests are not different and either test can be used.


here's a reference explaining how the paired t-test is done.


<a href = "https://www.jmp.com/en_us/statistics-knowledge-portal/t-test/paired-t-test.html" target = "_blank">https://www.jmp.com/en_us/statistics-knowledge-portal/t-test/paired-t-test.html</a>