Question

Suppose the population standard deviation is σ = 5 σ=5 , an SRS of n = 100 n=100 is obtained, and the confidence level is chosen to be 98%. The margin of error for estimating a mean μ μ is given by:

Answer 1

Answer:

The margin of error for estimating a mean μ is 1.1625.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.01 = 0.99$, so $z = 2.325$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

So

$M = 2.325*\frac{5}{\sqrt{100}} = 1.1625$

The margin of error for estimating a mean μ is 1.1625.