The difference in the Organic Chemistry final exam scores between last semester
ID: 3207262 • Letter: T
Question
The difference in the Organic Chemistry final exam scores between last semester and three years ago will be analyzed by the dean. Although the standard deviations of these populations are unknown, the dean has evidence that they are equal. A sample of 32 of these scores from last semester had a mean of 68.9 and standard deviation of 4.4, and a sample of 40 scores from three years ago had a mean of 70.2 and standard deviation of 5. A claim is made that the mean final exam score from last semester (11 ) is less than the mean final exam score from three years ago (22 ).
find test statistic and P-Value.
Explanation / Answer
This is a case of lower tailed test:
H0: 1 ³ 2
H1: 1 < 2
S2P=(n1-1)S12+(n2-1)S22/(n1-1)(n2-1)
=(31)(4.4)^2+(39)(5)^2/(31)(39)
=600.16+975/1209
=1575.16/1209
=1.30
t=(X1-X2)-(µ1- µ2)/sqrt(S2P)(1/n1+1/n2)
68.9-70.2/sqrt(1.30)(1/32+1/40)
-1.3/0.2704
-4.81
The P-Value is < .00001.