Question

A store owner is interested in opening a second shop. She wants to estimate the true average daily revenue of her current shop to decide whether expanding her business is a good idea. The store owner takes a random sample of 60 days over a six-month period and finds that the mean revenue of those days is 3,472.00 dollars with variance 315,900.20 square dollars. Calculate a 95% confidence interval to estimate the true average daily revenue.

Answer 1

Every confidence interval has associated z value. As confidence interval increases so do the z value associated with it.
The confidence interval can be calculated using following formula:

`\overline{x} \pm (zs)/(\sqrt n)`
Where
`\overline{x}` is the mean value, z is the associated z value, s is the standard deviation and n is the number of samples.
We know that standard deviation is simply a square root of variance:

`s=√(315900.20)=\$562.05`
The confidence interval of 95% has associated z value of 1.960.
Now we can calculate the confidence interval for our income:

`3472.00\pm (1.960\cdot 562.05)/(√(60))\\ \$3472.00\pm142.22`