Question

The duration of telephone calls directed by a local telephone company: σ = 3.6 minutes, n = 560, 90% confidence. Round your answer to the nearest thousandth

Answer 1

Answer:

The margin of error for the confidence interval is of 0.25 minutes.

Step-by-step explanation:

With what we are given, the only thing that this question can be asked is the margin of error for the confidence interval of the mean duration of telephone calls directed by a local telephone company.

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

$\alpha = \frac{1-0.9}{2} = 0.05$

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 $1-0.05 = 0.95$, so $z = 1.645$

Now, find the margin of error M as such

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

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Using what we are given:

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

$M = 1.645*\frac{3.6}{\sqrt{560}}$

$M = 0.25$

The margin of error for the confidence interval is of 0.25 minutes.