Suppose administrators at a large school district decide to institute mandatory study halls at their middle schools in an effort to boost their students' academic performance. After one year, a guidance counselor decides to test whether students' grade point averages (GPAs) have improved compared to the previous school year. The counselor selects a random sample of 25 eighth-graders from throughout the district who were also enrolled in the district for seventh grade. He records their GPAs for grades seven and eight, and for each student, calculates the difference between the two. The counselor's data is summarized in the given table.
Variable
description Sample
mean Sample standard
deviation Standard
error estimate
seventh grade GPA x⎯⎯7= 2.89433 s7=0.51053 SE7=0.10211
eighth grade GPA x⎯⎯8=2.96493 s8=0.57332 SE8=0.11466
difference (8th - 7th) x⎯⎯=0.07060 s=0.23495 SE=0.04699
The counselor plans to use this information to conduct a matched-pairs t‑test of the null hypothesis H0:μ=0 against the alternative hypothesis H1:μ>0, where μ is the mean change in students' GPAs after mandatory study halls were instituted.
What is the t‑statistic for the counselor's test? Round your answer to three decimal places.
What is the p‑value for the counselor's test? Round your answer to four decimal places.
The counselor requires his results to be significant at a level of α=0.05. Complete the sentences below to state the decision and conclusion of his test based on your previous answers.
t=
p=