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: H 0: μ = 0 H a: μ > 0 where 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? Group of answer choices 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.

The P-value gives us the probability of getting the sample results, given that the null hypopthesis is true. That is why, it the P-value is small enough (smaller than the level of significance) is an indicator that the null hypothesis may not be true.

In this case, the P-value (0.028) is smaller than the level of significance (0.05), so the null hypothesis is rejected and we can conclude that there is significant difference for the studentes that take the SAT prep-class.

The population only include the students that take teh SAT prep-class, so it is not useful to compare to the performance of students that didn't take the class.

The right answer is:

"The one-day SAT prep class produces statistically significant improvements in SAT writing performance."