Question

What is the margin of error for a sample statistic for a population with a standard deviation of 5.75?

Answer 1

Explanation:

Given that there is a sample statistic for a population. Population std deviation sigma is given as 5.75.

Margin of error = z critical value * std error

For standard error we must know the sample size n.

Std error =
`(\sigma)/(√(n) ) =(5.75)/(√(n) )`

Margin of error = Z critical * std error =
`1.96*(5.75)/(√(n) )` for 95%

=
`2.58*(5.75)/(√(n) )` for 99%

Z critical = 1.96 for 95% and 2.58 for 99%

Hence margin of error =

Answer 2

Margin of error =z-score value for chosen confidence level×population standard deviation

Assuming a 95% confidence level , then

z=1.96

standard deviation=5.75

Margin of error= 1.96×5.75=11.27