```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.
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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