An economist found that a random sample of 42 high school teachers had an average annual salary of $56,490. A previous study showed that the population standard deviation is $4150. Calculate the margin of error, E, for a 99% confidence interval for µ, the average annual salary of all high school teachers.

Question

An economist found that a random sample of 42 high school teachers had an average annual salary of $56,490.  A previous study showed that the population standard deviation is $4150. Calculate the margin of error, E, for a 99% confidence interval for µ, the average annual salary of all high school teachers.

PsyDAG · Answer

99% = mean ± 2.575 SEm

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. To include each end, double proportion.