A private school promoted itself by advertising that its graduates had a higher
ID: 3219802 • Letter: A
Question
A private school promoted itself by advertising that its graduates had a higher average SAT verbal score than the national average. The national average is a score of 450 with a standard deviation of 75. At the end of the school year, the Parent-Teacher Association (PTA) decided to see if the SAT scores for students at the school were higher than the national average. It was found that the average SAT verbal score for 80 graduating seniors from this private school was 532. Use the .05 significance level to determine if scores from the students at this private school were higher than the national average.
A) What is the appropriate test for this data?
B) Conduct the appropriate hypothesis test. Only hand calculate if you choose a z-test and then follow the five steps of hypothesis testing and provide a drawing. Otherwise, use SPSS.
C) Give an interpretation of this data (one sentence conclusion of the hypothesis test that should be free of statistical jargon) and report the statistics in APA format.
D) Explain how you came to your conclusion about the null.
SS = 132.45
SD = 55.1
Explanation / Answer
(A) Ho: 450 versus Ha: > 450
(B)
Data:
n = 80
= 450
s = 75
x-bar = 532
Hypotheses:
Ho: 450
Ha: > 450
Decision Rule:
= 0.05
Critical z- score = 1.644853627
Reject Ho if z > 1.644853627
Test Statistic:
SE = s/n = 75/80 = 8.385254916
z = (x-bar - )/SE = (532 - 450)/8.38525491562421 = 9.779070622
p- value = 0
Decision (in terms of the hypotheses):
Since 9.779070622 > 1.644853627 we reject Ho and accept Ha
(C) Conclusion (in terms of the problem):
It appears that scores from the students at this private school are higher than the national average.
(D) Since the p- value < 0.05, we rejected the null hypothesis.
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