SOLUTION: From a very large population (normally distributed), a random sample of 8 students had taken. Following table shows students’ grades for an exam before the term starts and anothe

Question 1160585: From a very large population (normally distributed), a random sample of 8 students had taken. Following table shows students’ grades for an exam before the term starts and another exam right after the term.
Student Before-Term Exam After-Term Exam 1 75 80
2 85 70
3 65 55
4 45 65 5 55 65 6 60 70 7 70 80 8 80 60
a) (10 Points) Find a 95% confidence interval estimate of the mean improvement in the scores. Do you think that lectures during the term help to improve student grades?
b) (15 Points) Test the hypothesis at the 5% significance level that the population mean grade for After-Term Exam is at least 70.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Do a paired t-test
changes are =5, -15, -10, +20, +10, +10, +10, -20
they add to 10
mean 1.25 s=14.33
95/5 t-interval is (-10.73, 13.23)
Since 0 is in the interval, there is no evidence that lectures during the term helped improve student grades, or at least there is insufficient evidence to conclude that there was a difference.
for b, do a t-test t=-0.6 with p-value 0.72 (1-way test) and insufficient evidence to conclude that the after-term exam mean is at least 70.
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