Please Help!

Question

A sample of 350 orders for take out food at a local pizzeria found that the average cost of an order was $27 with s=$16. Find the margin of error, if we use a 95% confidence interval, for the average cost of an order. How do I figure this out?

Answer 1

Hi Destiny,

 

The margin of error for a 95% confidence level can be found with the equation

 

E = t_c s/√(n)

 

s is the standard deviation you were given, $17

n is the sample size given, 350 orders

t_c is the critical value of the t distribution, which you can find with a chart or calculator corresponding to 95% confidence.

 

With 95% = 0.95 confidence, that means we will reject 5% = 0.05 total outside of the confidence interval. The chart I have lists areas in 2 tails across the top = 0.05. This also corresponds to 0.05/2 = 0.025 in each tail.

 

The degrees of freedom required for the t chart is the sample size n minus 1, 350-1 = 349. My chart only lists 300 and 400 at that level, so choose conservatively, 300.

 

t_c = 1.968

 

Plug these in and you get the error estimate you were looking for.