SOLUTION: A statistics department within a university changed its curriculum degree requirements. One of the professors within the department expressed concern that this change would result

Question 90119: A statistics department within a university changed its curriculum degree requirements. One of the professors within the department expressed concern that this change would result in lower statistical skills among students. Students in the program before the change took place demonstrated a mean of 70 points on statistics proficiency exam. Thirty-six students in the new program took the proficiency exam and had the following scores:
68 68 78 61 58 72
62 65 53 57 52 76
66 54 58 81 76 78
75 81 88 48 76 59
61 80 78 67 80 58
77 56 70 66 72 79
Do the data (mean = 68.16, standard deviation = 10.25) indicate that the new curriculum degree requirements lower statistical proficiency exam scores? Use the 5% level of significance.

Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!
Do the data (mean = 68.16, standard deviation = 10.25) indicate that the new curriculum degree requirements lower statistical proficiency exam scores? Use the 5% level of significance
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Ho: mu=70
Ha: mu<70
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Critical Value for alph=5%: -1.645
Test Statistic:
z(68.16)= (68.16-70)/[10.25/sqrt(36)] = -1.84/1.708=-1.077
p-value = 0.14
Since p>alpha, fail to reject Ho.
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Conclusion: This test does not give significant statistical evidence
that the mean of scores has changed.
Cheers,
Stan H.