Question

Suppose we want to assess the effect of a one-day SAT prep class at a 5% level of significance. Scores on the SAT writing exam can range from 200 to 800. A random sample of 50 students takes the SAT writing test before and after a prep class. We test the hypotheses: LaTeX: H_0 H 0 : LaTeX: \mu=0 μ = 0 LaTeX: H_a H a : LaTeX: \mu>0 μ > 0 where LaTeX: \mu μ is the mean of the difference in SAT writing scores (after minus before) for all students who take the SAT prep class. The sample mean is 5 with a standard deviation of 18. Since the sample size is large, we are able to conduct the T-Test. The T-test statistic is approximately 1.96 with a P-value of approximately 0.028. What can we conclude? The one-day SAT prep class is associated with statistically significant improvements in SAT writing performance. Students taking a one-day SAT prep class performed significantly better on the SAT writing exam than students who did not take the class. Students taking a one-day SAT prep class do not show statistically significant improvements in their SAT writing performance. Scores only increased by 5 points, which is not significant on an exam where scores can range from 200 to 800. The one-day SAT prep class produces statistically significant improvements in SAT writing performance.

Answer 1