John is running a study on whether a particular SAT training class is effective. The students take the SAT before and after taking the class. The 95% confidence interval for the difference in scores (after - before) is [5, 15]. Which of the following is NOT true?

a. There is statistically significant evidence that the training class increases SAT scores.

b. The average increase in SAT score among the students was 10.

c. This is an example of a paired design.

d. The training class caused a big improvement in the students' SAT scores.

If John is running a study on whether a particular SAT training class is effective, the students take the SAT before and after taking the class and the 95% confidence interval for the difference in scores (after - before) is [5, 15], then the statement which is NOT true is 'The training class caused a big improvement in the student's SAT scores.' The answer is option d.

Given that the 95% confidence interval for the difference in scores (after - before) is [5, 15], we can infer that the training class is effective in increasing the SAT scores of the students. The average increase in the SAT score among the students was 10, which means that the students who took the training class have a higher average score than those who did not. Therefore, option (a) is true.
A paired design is a type of experiment where two groups of subjects are paired together and compared to each other. In a paired design, each subject receives both treatments or is observed twice. The 95% confidence interval is defined as the range of values in which 95% of the observed data is likely to fall.
The confidence interval provides a range of values that can be considered plausible estimates of the population parameter. Thus, option (d) is not true.

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