For each question, state the null hypothesis, determine the type of test to perform, test the null hypothesis (α = 0.05), and report relevant values (degrees of freedom, p-value, etc.).
A volleyball coach measures players’ vertical jump (in inches) before and after a 6-week training program.
| Player | Before | After |
|---|---|---|
| 1 | 22 | 24 |
| 2 | 24 | 26 |
| 3 | 20 | 22 |
| 4 | 23 | 25 |
| 5 | 21 | 22 |
| 6 | 25 | 27 |
| 7 | 22 | 23 |
| 8 | 19 | 21 |
| 9 | 23 | 24 |
| 10 | 21 | 22 |
before <- c(22, 24, 20, 23, 21, 25, 22, 19, 23, 21)
after <- c(24, 26, 22, 25, 22, 27, 23, 21, 24, 22)Two study apps are tested. Students are randomly assigned and their quiz scores (out of 100) are recorded.
app_A <- c(78, 82, 85, 80, 79, 83, 81, 84)
app_B <- c(80, 79, 83, 81, 82, 78, 84, 80)A national tutoring company claims that their program improves students’ SAT scores by an average of 100 points.
A random sample of 10 students who completed the program shows the following score improvements:
85, 110, 95, 120, 70, 105, 90, 115, 80, 100
improvements <- c(85, 110, 95, 120, 70, 105, 90, 115, 80, 100)Two training programs are compared.
Program A:
Program B:
(You may assume 48 degrees of freedom.)