SOLUTION: A high school math teacher wants to assess the effectiveness of a new teaching method for improving students’ algebra skills. She selects a random sample of 8 students from her

Question 1203947: A high school math teacher wants to assess the effectiveness of a new teaching method
for improving students’ algebra skills. She selects a random sample of 8 students
from her class and administers a pre-test to evaluate their algebra knowledge. After
introducing the new teaching method over the course of a semester, she administers a
post-test to the same students to measure any improvements in their algebra skills.
Student 1 2 3 4 5 6 7 8
Pre-Test Score 50 45 60 65 75 92 86 88
Post-Test Score 52 50 65 62 71 90 89 90
Construct a 95% confidence interval for the difference in means.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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 https://www.mathportal.org/calculators/statistics-calculator/t-test-calculator.php

here are the results.

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.

https://www.jmp.com/en_us/statistics-knowledge-portal/t-test/paired-t-test.html

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