Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee at local fast food restaurants. Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg. If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

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

Now, we have to find z in the Ztable as such z has a pvalue of .

That is z with a pvalue of , so Z = 1.96.

Now, find the margin of error M as such

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

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when . So

Dividing both sides by 0.5

Rounding up

We would have to take a sample of 62 to achieve this result.