SOLUTION: it is known that the variance of a population equals 1936. A random sample of 121 has been taken from the population. there is a 0.95 probability that the sample mean will provid

Algebra ->  Probability-and-statistics -> SOLUTION: it is known that the variance of a population equals 1936. A random sample of 121 has been taken from the population. there is a 0.95 probability that the sample mean will provid      Log On


   

Question 926883: it is known that the variance of a population equals 1936. A random sample of 121 has been taken from the population. there is a 0.95 probability that the sample mean will provide a margin of error of?
Found 2 solutions by Theo, ewatrrr:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
variance = 1936
standard deviation = square root of variance = 44
standard error = standard deviation divided by square root of sample size.
sample size = 121
square root of sample size = 11
standard error = 44/11 = 4
critical z factor for a confidence interval of .95 is equal to plus or minus 1.96.
margin of error equals critical z factor * standard error = 4 * 1.96 = 7.84
confidence interval equals mean plus or minus margin of error equals mean plus or minus 7.84.
here's a reference that has an example that will help you to understand better if you need to.
http://stattrek.com/estimation/margin-of-error.aspx



Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
ME = 1.96 sqrt(1936/121) = 1.96(4) = 7.84
95% chance ME = ± 7.84