The Comprehensive Assessment of Outcomes in Statistics (CAOS) exam is an online multiple-choice test on concepts covered in a typical introductory statistics course. Students can take a pretest version before instruction and then a posttest version after instruction. Fter taking the class, the pretest and posttest scores are compared to assess student learning in the course. For a random sample of 10 students who took the class from Professor X, the posttest scores increased over the pretest score by an average of 14 percentage points, with a standard deviation of 6.4 points. a) What additional information (if any!) do we need to know in order to use t-based methods from this data set? b) Compute a 95% confidence interval for the mean improvement in CAOS scores for students who took the class from Profesor X. c) The developers of the CAOS exam report that, for all students who have taken the CAOS exam (and not just Professor X’s students), the mean improvment is 10.1. Do we have evidence to plausibly conclude that Professor X’s students improved more than the typical student who takes the CAOS exam?
The Comprehensive Assessment of Outcomes in Statistics (CAOS) exam is an online multiple-choice test
on concepts covered in a typical introductory statistics course. Students can take a pretest version before
instruction and then a posttest version after instruction. Fter taking the class, the pretest and posttest scores
are compared to assess student learning in the course.
For a random sample of 10 students who took the class from Professor X, the posttest scores increased over
the pretest score by an average of 14 percentage points, with a standard deviation of 6.4 points.
a) What additional information (if any!) do we need to know in order to use t-based methods from this
data set?
b) Compute a 95% confidence interval for the mean improvement in CAOS scores for students who took
the class from Profesor X.
c) The developers of the CAOS exam report that, for all students who have taken the CAOS exam (and
not just Professor X’s students), the mean improvment is 10.1. Do we have evidence to plausibly
conclude that Professor X’s students improved more than the typical student who takes the CAOS
exam?
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