8. I am interested in whether
8. I am interested in whether or not students who fail thisstatistics course one semester do better on their teststhe second time they take the class. To examine this, I record thetest scores for a sample of 10 students who took the class lastsemester and are repeating the class this semester. The test scoresfor these 10 students are reported below for last semester and thissemester. Conduct the appropriate hypothesis test to determinewhether or not student scores are significantly greaterfor students taking the class the second semester compared to theirscores the first semester. State a type of a test, the null andresearch hypotheses, the critical value, obtained t statistic, yourconclusion, and interpret your results (Alpha = .05). (6pt)
|
Student |
Last Semester |
This Semester |
|
A |
65 |
78 |
|
B |
70 |
72 |
|
C |
54 |
66 |
|
D |
66 |
57 |
|
E |
42 |
50 |
|
F |
69 |
82 |
|
G |
70 |
70 |
|
H |
64 |
62 |
|
I |
39 |
55 |
|
J |
53 |
60 |
Answer:
Ho : µ1 – µ2 = 0 Ha : µ1-µ2 < 0 Level of Significance , α = 0.05 Sample #1 —-> sample 1 mean of sample 1, x̅1= 59.20 standard deviation of sample 1, s1 = 11.55 size of sample 1, n1= 10 Sample #2 —-> sample 2 mean of sample 2, x̅2= 65.20 standard deviation of sample 2, s2 = 10.30 size of sample 2, n2= 10 difference in sample means = x̅1-x̅2 = 59.2000 – 65.2 = -6.00 pooled std dev , Sp= √([(n1 – 1)s1² + (n2 -1)s2²]/(n1+n2-2)) = 10.9473 std error , SE = Sp*√(1/n1+1/n2) = 4.8958 t-statistic = ((x̅1-x̅2)-µd)/SE = ( -6.0000 – 0 ) / 4.90 = -1.226 Degree of freedom, DF= n1+n2-2 = 18 p-value = 0.1181 [ excelfunction: =T.DIST(t stat,df) ] Conclusion: p-value>α , Do not reject nullhypothesis There is not enough evidence to say taht student scores aresignificantly greater for students taking the class thesecond semester compared to their scores the first semester.
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