A statistics instructor likes to assign the material as reading in the textbook and then give a pretest before covering the mate
rial in class to discover which topics the students did not master from the reading. About an equal number of students mastered "most," "some," or "almost none" of the material from reading the textbook based on the pretest results. Then the instructor covers the material in class and assigns homework for the students to practice what they have learned. After the students complete the homework, they work with each other and the teacher in class on the problems they did not understand. Finally, after all students have mastered most of the material, she gives the same exam as a posttest. Which one of the following data sets would you expect to have the smaller standard deviation?
a. The student’s scores on the pretest.
b. The student’s scores on the posttest.
c. We expect the standard deviations to be about the same.
b. The student's scores on the posttest would have a smaller standard deviation.
Step-by-step explanation:
The first test is taken before the material is covered in class so we expect the standard deviation to be high because not everyone's scores would be lying close to the mean. Equal number of students mastered most, some or almost none of the material from reading the textbook based on the pretest result. this means the data is varying, so the standard deviation is large.
Whereas, after the teacher has taught the material and given the homework, they must have understood most of the material. The test they take after teaching as a post test. The results of the post test would have a smaller standard deviation as most of the students would have scored good. Hence, the student's scores on the posttest would have a smaller standard deviation.
