a random sample of 22 fifth grade pupils have a grade point average of 5.0 in ma
ID: 3153313 • Letter: A
Question
a random sample of 22 fifth grade pupils have a grade point average of 5.0 in maths with a standard deviation of 0.452, wheras marks range from 1 (worst) to 6 (excellent). The grade point average of all fifth grade pupils of the last five years is 4.7. Is the GPA of the 22 pupils different from the populations' GPA?
a) identify independent and dependent variables
b) using symbols, state the null and alternative hypothesis
c) determine the critical region and conduct a t-test
d)state your decision concerning the null hypothesis
Pupil Grade Points 1 4.0 2 4.5 3 3.8 4 4.5 5 3.0 6 2.8 7 4.5 8 4.75 9 3.0 10 4.0 11 5.0 12 3.3 13 4.8 14 5.0 15 4.7 16 4.5 17 4.7 18 5.0 19 5.0Explanation / Answer
A) PUPIL ARE THE INDEPENDENT VARIABLE WHERE AS THE GRADE IS THE DEPENDENT VARIABLE
B) THE HYPOTHESIS WILL BE H0 = U = 4.7
HA= U >4.7
C) ALPHA = 0.05
DEGREE OF FREEDOM = 22-1 = 21
IT IS RIGHT TAIL TEST
THEREFORE FROM THE T TABLE THE CRTITICAL REGION = T>1.72
T TEST = (X-MEAN)/(STANDARD DEVIATION/SQRT(N)
= (5-4.7)/(0.452/SQRT(22)) = 3.125
D) AS BY THE T TEST, T = 3.125 > 1.72 THEREFORE WE WILL REJECT THE NULL HYPOTHESIS
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