Consider an experiment in which a Community College administers their College Algebra courses with the exact same Final exam. Administrators hope that the average score will not vary dramatically between the class sections. Four sections of the class (S1, S2, S3, S4) are used, from which 5 random exam percentages were considered. The data were as follows: Section S 3 was taught by a first-time professor and the remaining sections by a seasoned professor. Suppose we want to test whether mean section score from seasoned professor's sections are more than the mean score from the first-time professor. The contrast corresponding to this comparison is 1 = a 1 1 + a 2 2 + a 3 3 + a 4 4 where i is the mean section score from S t h i section. What are the values of the coefficients a 1 , a 2 , a 3 and a 4 ? What are the corresponding hypotheses of interest? Find the test statistic to test the hypothesis. Include any relevant output. What is the distribution of your test statistic under the true null hypothesis?

Consider the contrast to compare the average effect of S1 and S2 (evening classes) to the effect of S4 (morning class) on mean scores

2=b11+b22+b33+b44

Are 11and 22orthogonal contrasts?

Is the linear comparison independent of the linear comparison 1 ?