While teaching a unit on fractions, a fifth-grade teacher
regularly administers a pre-test at the beginning of the unit and a
post-test at the end of the unit. The teacher then
calculates the improvement in scores for each student (post-test
score minus pre-test score).
For the school district, the standard for improvement in scores
is 15 points. The teacher would like to test whether
improvement in scores for his/her students is on average higher
than the district standard at a significance level of
0.05.
For a random sample of the teacher's students, the mean
improvement is 28.1 points, with a standard deviation of 26.4
points. There are 16 students in the sample.
Based on the p-value associated with the calculated test
statistic, which of these conclusions is appropriate?
Select one:
a. There is sufficient evidence at the 0.05 level of
significance to conclude that the improvement in scores of this
teacher's students is higher than that expected for the
district.
b. There is not sufficient evidence at the 0.05 level of
significance to conclude that the improvement in scores of this
teacher's students is different from that expected for the
district.
c. There is sufficient evidence at the 0.05 level of
significance to conclude that the improvement in scores of this
teacher's students is lower than that expected for the
district.