To determine if his teaching method increases students' learning, a professor administers a pretest to his class at the beginning of the semester and then a posttest at the end of the semester. The results from 10 randomly chosen students are given below. Let Population 1 be the Pretest scores and Population 2 be the Posttest scores.
Test Scores
Pretest, Posttest
50, 71
73, 82
64, 80
50, 62
86, 92
76, 71
60, 74
71, 80
76, 81
70, 68
Step 2 of 2: interpret the confidence interval obtained in Step 1.
Answer (1)
The teaching method likely increases students' learning.
Explanation
Understand the problem and data We are given pretest and posttest scores for 10 students and need to determine if the teaching method increases students' learning. We will interpret the confidence interval obtained in Step 1 to make this determination. From the previous calculations, we have the 95% confidence interval for the difference between posttest and pretest scores.
State the confidence interval The calculated 95% confidence interval for the mean difference between posttest and pretest scores is (2.8245, 14.1755). This means we are 95% confident that the true mean difference between posttest and pretest scores lies within this interval.
Interpret the confidence interval Since both the lower and upper bounds of the confidence interval are positive (i.e., greater than zero), it indicates that, with 95% confidence, the posttest scores are significantly higher than the pretest scores. This suggests that the teaching method likely increases students' learning.
Conclusion The 95% confidence interval (2.8245, 14.1755) does not contain zero, indicating a statistically significant difference between the pretest and posttest scores. Since the interval is entirely above zero, we conclude that the teaching method is likely effective in increasing students' learning.
Examples
Consider a scenario where a company implements a new training program for its employees. By administering pre-training and post-training tests, they can assess the effectiveness of the program. If the confidence interval for the difference in scores is entirely above zero, it suggests the training program is likely beneficial. Conversely, if the interval contains zero or is below zero, the company might need to re-evaluate the training program's effectiveness. This approach helps in making data-driven decisions about the value of educational or training interventions.
