A teacher gives a third grade class of n=16 a reading skills test at the beginning of the school year. To evaluate the changes that occur during the year, students are tested again at the end of the year. Their test scores revealed an average improvement of MD=4.7 points.
a. If the variance for the difference scores is s2=144, are the results sufficient to conclude that there is significant improvement? Use a one-tailed test with a=0.05.
b. If the variane for the difference score is reduced to s2=64,are the result sufficient to conclude that there is signifficant improvement? Use a two tailed test with aplha=.05
c. Describe the effect on reducing the variance of the difference score.