Question

Mika is a local farmer who is interested in how often residents in her town go to a farmer's market each month. She surveys 124 families and finds that, on average, those families visit a farmers' market 4.2 times per month with a sample standard deviation of 1.3. If Mika wants to be 99% confident (z=2.58) using this sample, what should her margin of error be and what does it mean?

Answer 1

Answer:

The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.

Step-by-step explanation:

Margin of error

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

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

Standard deviation of 1.3

This means that $\sigma = 1.3$

She surveys 124 families

This means that $n = 124$

Margin of error and meaning:

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

$M = 2.58\frac{1.3}{\sqrt{124}}$

$M = 0.3012$

The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.