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
"H_0: \\mu_d\\le0\\\\\nH_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.
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