Chapter 10 Frappy
Jessica wondered if elementary school students tend to write more when they are given a larger
amount of space in which to write. To investigate, she asked 100 fourth and fifth grade students
to respond to the following prompt: “Do you like recess? Why or why not?” About half of the
students were randomly assigned to use a larger 1/4-sheet of paper to write their response and the
remaining students were assigned a smaller 1/6-sheet of paper. After the students finished,
Jessica counted the number of words in each response. Summary statistics for each group are
shown in the table.
Group
N
Larger sheet 46
Smaller sheet 54
Mean Standard Deviation
18.3 8.5
16.9 7.9
1. Calculate and interpret a 95% confidence interval for the difference in mean number of
words written for students like these who are asked to respond to the prompt on either a
1/4-sheet of paper or a 1/6-sheet of paper.
a. Conditions:
Random: The prompt states that the students were randomly assigned to write on
either the ¼-sheet of paper or the ⅙-sheet of paper.
10%: Since this is an experiment, and the students were assigned to either group,
independence is assumed.
Large Counts: Both the sample size for the larger sheet of paper and the sample
size for the smaller sheet of paper is greater than 30, which confirms normalcy in
the data.
Calculations:
2 Sample T Interval(x1=18.3, sx1=8.5, n1=46, x2=16.9, sx2=7.9, n2=54,
C-level=0.95)
Correction: Must use manual formula, not calculator inputs.
(-1.879, 4.679)
We are 95% confident that the interval from -1.879 to 4.679 contains the true
difference (specify what is subtracted by what) in the number of words written
from students who were asked to respond to the prompt on a ¼-sheet of paper and
the number of words written from students who were asked to respond to the
prompt on a ⅙-sheet of paper.
2. Based only on the confidence interval from part (a), is there convincing evidence that the
size of the paper affects the mean number of words written for students like these?
a. Since the 95% confidence interval contains the value of 0, as well as both values
greater than and less than 0, we do not have convincing evidence that the size of
the paper affects the mean number of words written for fourth and fifth grade
students.