CAOS Comparisons Anarticle by the developers of the CAOS exam described in Exercise C.68 gives benchmark data based on a very large number of students taking the CAOS pretest and posttest. The mean score on the CAOS pretest was 44.9 and the mean on the CAOS postest was 54.0 for an average improvement of 9.1 points. We treat these values as population means for all students taking the CAOS exams.
(a) Using the data in Table C.14 and CAOSExam for a sample from one instructor, is there enough evidence to conclude at the 5% level that this instructor€™s students have a mean score on the posttest that is higher than 54.0?

Table C.14

(b) Can we conclude that this instructor was starting with stronger students? Test if the mean score for this instructor€™s students on the CAOS pretest is higher than the benchmark mean of 44.9 points, using a 5% significance level.
(c) Can we conclude, at the 5% level, that the mean improvement from pretest to posttest for students with this instructor is higher than the national norm of 9.1 points?

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Student D 42.5 Pretest Posttest 42.5 47.5 37.5 55 40 45 47.5 65 60 37.5 55 42.5 60 55 80 85 72.5 57.5 57.5