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 40 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¯= 2.64796 s=0.45763 SE=0.07236 eighth grade GPA x¯=2.78543 s=0.54764 SE=0.08659 difference (8th - 7th) x¯=0.13747 s=0.34586 SE=0.05469 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'
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 40 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¯= 2.64796 | s=0.45763 | SE=0.07236 |
| eighth grade GPA | x¯=2.78543 | s=0.54764 | SE=0.08659 |
| difference (8th - 7th) | x¯=0.13747 | s=0.34586 | SE=0.05469 |
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?
complete the sentence
The counselor should __________ his ___________ hypothesis. There is ____________ evidence that the mean difference in GPA from seventh grade to eighth grade for _______ is _______ _________
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