Question 279755: The average math SAT score is 518 with a standard deviation of 115. A particular high school claims that its students have unusually high math SAT scores. A random sample of 50 Students from this school was selected and the mean math SAT was 535.
a) Is the high school justified in its claim? Justify your answer.
b) Which is more likley to happen, one student making a math SAT score of 535 or a group of 50 having a mean math SAT score of 535? Justify your answer.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The average math SAT score is 518 with a standard deviation of 115. A particular high school claims that its students have unusually high math SAT scores. A random sample of 50 Students from this school was selected and the mean math SAT was 535.
Ho: u <= 518
Ha: u > 518
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t(535) = (535-518)/[115/sqrt(50)] = 1.1068
p-value = P(t > 1.1068 with df = 49) = tcdf(1.1068,10,49)= 0.1369
Conclusion: Since the p-value is above 10%, fail to reject Ho
at the 13% significance level.
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a) Is the high school justified in its claim? Justify your answer.
Ans: No
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b) Which is more likely to happen, one student making a math SAT score of 535 or a group of 50 having a mean math SAT score of 535?
t(535) = (535-518)/115 = 0.1478
t(535) = 0.1478 is the t-score for the individual.
t(535) = 1.1068 is the t-score for the group of 50.
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The score closer to the mean is the more likely to occur;
that would be the score for the individual.
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Cheers,
Stan H.
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