Answer to Question #342749 in Statistics and Probability for athena

Question

a reading center demands that the students will perform better on a standardized reading test after going through the reading test after going through the reading course offered by their center. the table shows the reading scores of 5 students before and after the course. at α=0.10, is there enough evidence to conclude that the students’ scores after the course are better than the scores before the course?

STUDENT BEFORE AFTER

1 85 88

2 96 85

3 70 89

4 76 86

5 81 92

Answer 1

$H_0: \mu_d\le0\\ H_a:\mu_d>0$ (Claim)

d=(score before-score after)

$\=d=\frac{\sum{d}}{n}=-32/5=-6.4$

$s_d=\sqrt{\frac{n(\sum{d^2})-(\sum{d})^2}{n(n-1)}}=\sqrt{\frac{5(712)-1024}{20}}=11.26$

We can find critical value $t_0$ using t-table (in this problem $\alpha=0.10, df=5-1=4$ ):

$t_0=1.533$

The standardized test statistic is:

$t=\frac{\=d-\mu_d}{s_d/\sqrt{n}}=\frac{-6.4-0}{11.26/\sqrt5}=-0.254$

Since $t<t_0 (-0.254<1.533)$, $H_0$ is not rejected.

So there is not enough evidence at the 10% level to support the claim that the student`s scores after the course are better than the scores before the course.