Ten randomly selected college students, who participated in a learning community, were given pre-self-esteem and post-self-esteem surveys. A learning community is a group of students who take two or more courses together. Typically, each learning community has a theme, and the faculty involved coordinate assignments linking the courses. Research has shown that the benefits of higher self-esteem, higher grade point averages (GPAs), and improved satisfaction in courses, as well as better retention rates, result from involvement in a learning community. The scores on the surveys are as follows.
Student 1 2 3 4 5 6 7 8 9 10
Prescore 11 15 20 15 16 19 21 21 14 22
Postscore 22 16 16 15 21 14 12 17 21 16
Lower scores indicate higher self-esteem. Does this sample of students show sufficient evidence that postscores were lower than prescores indicating self-esteem was higher after participation in a learning community? Use the 0.05 level of significance and assume normality of scores.
Find the p-value. (Give your answer correct to three decimal places.)