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 Number Mean Standard Deviation
Larger sheet 46 18.3 8.5
Smaller sheet 54 16.9 7.9
(a) 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.
(b) 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?