Question

A company that sponsors LSAT prep courses would like to be able to
claim that their courses improve scores. To test this, they take a
sample of 8 people, have each take an initial diagnostic test, then
take the prep course, and then take a post-test after the course.
The test results are below (scores are out of 100%):

Person 1,2,3,4,5,6,7,8
Post-Test 86,81,80,68,80,59,64,67
Initial Test 73,74,66,60,76,60,65,62

Is there evidence, at an α=0.075 level of significance, to conclude that the prep course
improves scores? Carry out an appropriate hypothesis test, filling
in the information requested. (Arrange your data so that the
standardized test statistic is for the change from the initial test
to the post-test.)
A. The value of the standardized test statistic:
Note: For the next part, your answer should use interval notation.
An answer of the form (−∞,a) ( − ∞ , a ) is expressed (-infty, a),
an answer of the form (b,∞) ( b , ∞ ) is expressed (b, infty), and
an answer of the form (−∞,a)∪(b,∞) ( − ∞ , a ) ∪ ( b , ∞ ) is
expressed (-infty, a)U(b, infty).
B. The rejection region for the
standardized test statistic:
C. The p-value is
D. Your decision for
the hypothesis test: A. Reject H0 H 0 . B. Do Not Reject H0 H 0 .
C. Reject Ha H a . D. Do Not Reject Ha H a .

Answer 1

given that

sample size =n=8

Let

The difference in Scores=Post Test - Initial test

we need to test those courses improves the score so we need to test that difference of mean score is more than ZERO or not Hence

from the data we have

sample mean of difference =md=6.125

sample SD of difference =Sd=5.62

A)

test statistics is given by

t will have DF=n-1=8-1=7

B)

since test is right tailed and level of significance =0.075

P(t>critical value)=0.075

P(t>1.62)=0.075

so critical value =1.62

Hence we reject H0 if t>1.62

C)

P-Value =P(t>3.084) =0.009

D)

since P value is less than level of significance hence we reject H0 so

A. Reject H0