Question

assume that population means are to be estimated from the samples described. use the sample results to approximate the margin of error and 95% confidence interval.sample size= 81sample mean= 83sample standard Deviation= 10

Answer 1

The formula for the margin of error is given by :

$MOE=z\frac{SD}{\sqrt[]{n}}$

Where SD = standard deviation

n = sample size

z = z-value at 95% confidence level which is always equal to 1.96

and MOE = Margin of Error

Solving for the margin of error :

$MOE=1.96(\frac{10}{\sqrt[]{81}})=\pm2.18$

The margin of error is

$\pm2.18$

Solving for the confidence interval :

$CI=\operatorname{mean}\pm\text{MOE}$

CI = 83 - 2.18 = 80.82

CI = 83 + 2.18 = 85.18

So the confidence interval is 80.82 to 85.18