Suppose a sample of 256 was taken from a population with a standard deviation 96 centimeters. In this case, the sample mean will be within how many centimeters of the population mean 68% of the time?

A. 6
B. 4
C. 8
D. 10

Question

Suppose a sample of 256 was taken from a population with a standard deviation 96 centimeters. In this case, the sample mean will be within how many centimeters of the population mean 68% of the time?

A. 6
B. 4
C. 8
D. 10

amistre64 · Answer

well it seems we are talking about point estimators.

the standard error is a good point estimator for the population standard deviation.

the standard error is just a modification/adjustment of the sample standard deviation.  can you recall how it is modified?

amistre64 · Answer

well, i got most of the idea right :)

the standard error is an adjustment of sigma (population standard deviation)

hockeychick23 · Answer

oh ok so would it be 8% or did I calculate that wrong

amistre64 · Answer

standard error = sigma/sqrt(n)

so for the given population standard deviation (sigma) and a sample size (n) we have:

96/sqrt(256) = 6

since 68% of the data is about 1 standard deviation to the left and right of the mean, then we would expect that 68% of the means of the sample means would be 1 standard error from the mean.