SOLUTION: Many people believe that the average number of Facebook friends is 338. The population standard deviation is 43.2. A random sample of 50 high school students in a particular distri

Question 1200408: Many people believe that the average number of Facebook friends is 338. The population standard deviation is 43.2. A random sample of 50 high school students in a particular district revealed that the average number of Facebook friends was 350. At alpha=0.05, is there sufficient evidence to conclude that the mean number of friends is greater than 338?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
population average is assumed to be 338.
population standard deviation is 43.2
sample of 50 students reveals that the average number of facebook friends is 350.
test is to see if the average is greater than 338.
one tailed alpha is indicated on the high end because the text is for greater than.
at .05 alpha, on the high end, the critical z-score will be 1.644853626.
z-score formula is z = (x-m)/s
z is the z-score
x is the sample mean
m is the assumed population mean
s is the standard error.
standard error = standard deviation divided by square root of sample size = 43.2 / sqrt(50) = 6.209402589.
test z-score = (350 - 338) / 6.209402589 = 1.964185503.
since this is greater than the critical z-score, the test results are significant and the conclusion is that the verage is most probably greater than 338.
you could also test with alpha.
the results will be consistent with the critical z-score test.
the critical alpha is .05 on the high end.
the area to the right of the test z-score is .0247542216.
since this is less than the critical alpha, the results are, once again, considered significant, leading to the same conclusion.

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