1. CSU reports the average ACT score is 26.1 Suppose we think liberal arts students score higher on average in reading, so we sample 100 liberal arts students who took the ACT and ask them their score. The mean score among these 100 students was 27, with a standard deviation of 6. So, in our sample, they do better than 26, but maybe that's just due to chance because we only sampled 100 students! We will test this to see if the difference we observe is statistically significant. a. Our null hypothesis is that there is no true difference in scores between liberal arts students (if we could ask all of them) and CSU students in general. H0: Liberal arts student average = 26. Or, more formally: H0 = 26 What is the research hypothesis? Ha b. Use the formula for the standard error of the mean to show that the standard error is .6 (you will not receive credit if you do not show some work). Recall the formula is: c. New show that the zscore is 1.67. d. Based on the z-score, why can you not reject the null hypothesis and not be at least 95% confident that Liberal Arts students do better than the average CSU student? e. Finally, show that the 95% confidence interval on the SAT score is (25.8,282). This is the range of scores for which we are 95% sure that the true average of liberal arts students lies