Question

Two randomly selected groups of 200 students each were taught two different memorization methods over a four week period. At the end of four weeks a memorization test with a maximum possible score of 100 was given. The confidence interval of the difference in the two group population mean scores on the memorization test was (01-03). What statement best reflects the results of this study.

A) the results are not statistically significant, but are of practical significance
B) the results are statistically significant, but probably not of practical significance since the true population mean difference is a very small percentage of the total points possible (difference in points is 1% to 3% of the total points possible)
C) the results are statistically significant and also of practical significance since the true population mean difference in points is 1% to 3% of the total points possible.
D) the results are not statistically significant and also not of practical significance

Answer 1

The results showing a 1% to 3% difference between two memorization methods are statistically significant but not of practical significance due to the minor difference in mean scores. Option B correctly reflects this interpretation.

Step-by-step explanation:

The confidence interval of the difference in the two group population mean scores on the memorization test being (0.01-0.03) indicates that the true population mean difference is very small, namely 1% to 3% of the maximum possible test score. This difference is quite minor when considered in the context of the total points possible on the test.

Thus, if we are to make a judgment regarding the practical significance and statistical significance of the results, option B seems the most apt. The results are statistically significant, but probably not of practical significance since the true population mean difference is a very small percentage of the total points possible. Statistical significance speaks to the likelihood that the observed difference between groups is not due to sampling error, while practical significance refers to whether the difference is large enough to have real-world implications or utility.