in an effort to improve the mathematical skills of 10 studen

in an effort to improve the mathematical skills of 10 students, a teacher provides a weekly 1 hour tutoring for the students. a pretest is given before the sessions, and a posttest is given after the sessions. the results are shown below. at alpha equal to 0.01, can it be concluded that the sessions help to improve the students\' mathematical skills? Pretest: 83, 77, 94, 61, 84, 69, 70, 66, 82, 86. Posttest: 89, 80, 97, 82, 80, 72, 75, 79, 86, 94.

Solution

Null Hypothesis: Mu(Pretest) < Mu(Posttest)

Alternate Hypothesis : Mu(Pretest) >= Mu(Posttest)

Data1 : {83, 77, 94, 61, 84, 69, 70, 66, 82, 86}

Mean1 = 77.2

SD1 = 10.38

n1 = 10

Data2 : {89, 80, 97, 82, 80, 72, 75, 79, 86, 94}

Mean2 =83.4

SD2 = 8.03

n2=10

Standard Error : = sqrt((10.38^2/10) + (8.03^2/10)) = 4.15

t = (77.2 - 83.4) / 4.15 = -1.49

dF = 10 + 10 -2 = 18

P-value = 0.076

Since , P-value > 0.01

Failed to reject null hypothesis , may or may not be the fact that the sessions help to improve the students\' mathematical skills.