Based on the answer from C3, can you reflect on each of these separately for me please?
1.I think that Bobby should send in his ACT scores. The probability of scoring above a 30 on the ACTs is slightly more than 2.5%. I know this because 31 is two standard deviations from the mean and using the Empirical Rule this is the probability that approximates it. For the SATs, his score is slightly more than one standard deviation from the mean. This means that the probability of someone scoring better than him on the SATs is about 16%. He did better than most students on the ACT.
2.I think that Bobby should send his ACT score to his colleges. When Bobby’s ACT score is located on the normal curve it falls approximately two standard deviations above the mean score, but his SAT score is just over one standard deviation above the mean. Because his ACT score is further away from the mean, it makes his score of 30 stand out more when compared to other students. With the ACT score being almost two standard deviations away from the mean it means that approximately 2.5% of students scored higher than him, or stated differently, Bobby scored higher than 97.5% of students on the ACT test whereas he only scored better than approximately 85%% of students who took the SAT test. Comparatively speaking Bobby’s ACT test score will look better than his SAT test score and he should therefore send that score to his colleges.
E2– can you reflect on these for me please?
3.I do not think that there is sufficient evidence to conclude that SAT prep improves SAT scores. A random sample of 50 students may not be sufficient to generalize for the entire population. Since what is being compared is the mean of an entire population.Based on the graph whichcontains the means collected from 355 samples of 50 SAT Scores it shows that it was unlikely that students would score 1000.
4.Based on the graph of the means from 355 samples of 50 SAT scores, it is highly unlikely for a group of 50 randomly selected students to average 1000. There were not any sample means in the graph that were above 970. I calculated the probability of it happening (P(x>1000)=(1000-896)/174/sqrt50) and got 1.188×10^-5. This means that there is statistically significant evidence to show that the SAT program is effective.