SOLUTION: The average math SAT score is 511 with a standard deviation of 199. A particular high school calims that its students have unusually high math SAT scores. A random sample of 40 stu

Question 1176498: The average math SAT score is 511 with a standard deviation of 199. A particular high school calims that its students have unusually high math SAT scores. A random sample of 40 students from this school was selected, and the mean math SAT score was 555. Is the high school justified in its claim? Explain?
Find the Z-score and complete the explanation/statement
(Yes/No) because the z-score ([?]) is (unusual/not unusual) since it (lies / does not lie) within the range of a usual event, namely within (1,2,3 standard deviation) of the mean of the sample means.
(Round to two decimal places as needed)

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the z-score is z=(x bar-mean)/sigma/sqrt(n)
=(555-511)/199/sqrt(40)
=44*sqrt(40)/199
=1.40
The probability of finding a result this much or more extreme is 0.0810
It depends upon what criteria the tester wants to require from the school.
If the 5% level of significance is used, which would be (for a 1 way test) 1.645 or more sd s from the sample mean, then no, it is not unusual. If the 10% level is used, then it would be unusual.

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