An agency that offers tutoring students for students taking the SAT is intereste

Question

An agency that offers tutoring students for students taking the SAT is interested in evaluating the effectiveness of their programs. A random sample of 5 students is used to evaluate if their SAT score increases by more than 50 points after completing their program. The score of the 5 students before and after completing the program is shown below.

Using a significance level of 5%, What is the p-value of the Hypothesis test to determine if the training is effective in increasing the students score by more than 50 points ? (use 3 decimals)

Student 1 2 3 4   5 Score before the training 400 520 700 600 425 Score after the training 450 600 735 660 460

Explanation / Answer

Hypothesis:

H0 : d = 50

Ha : d > 50

Test statistics:

Before After dbar

400 450 -50

520 600 -80

700 735 -35

600 660 -60

425 460 -35

Mean -52

Before(1) After(2)

n 5 5

mean() 529 581

std. dev. 124.3181 124.6194206

SE(s/sqrt(n)) 55.5968 55.7315

dbar = (before) - (after) = -52

s(dbar) = 18.9077

SE = s(dbar)/sqrt(n) = 8.4558

Test Statisitcs, t = (dbar - 50)/SE = -12.0627

degrees of freedom = n-1 = 4

p-value = 0.0001

We reject the null hypothesis

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