SOLUTION: A report says that 82% of British Columbians over the age of 25 are high school graduates. A survey of randomly selected residents of a certain city included 1290 who were over the
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Question 1205265: A report says that 82% of British Columbians over the age of 25 are high school graduates. A survey of randomly selected residents of a certain city included 1290 who were over the age of 25, and 1012 of them were high school graduates.
Is the city's result of 1012 unusually high, low, or neither?
A) high
B) low
C) neither
I have only 2 changes to try. Please be sure that you haven't done any calculation error. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! p = .82
q = 1 - .82 = .18
your mean proportion is .82.
your standard error is sqrt(.82 * .18 / 1290) = .0106966632.
your sample mean is 1012/1290 = .784496124.
the z-score formula is z = (x-m)/s
in this problem .....
z = z-score
x = sample mean
m = assumed population mean
s = standard error.
the formula becomes z = (.784496124 - .82)/.0106966632 = -3.319154314.
area to the left of that z-score is equal to .0004515097405.
that is a very strong indication that the sample mean is less than the population mean in reality and that the difference between the sample mean and the population mean is not due to random variations in the mean of samples whose size is 1290.
a very strong alpha test is usually .01/2 = .005.
the test alpha of .0004515097405 is well below that, supporting the conclusion that the sample mean is clearly less than the assumed population mean.
selection B appears to be your answer.
the city's result is definitely lower than the report result of 82%.
