A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phylum. She wants to estimate the proportion using a 99% confidence interval with a margin of error of at most 0.01. How large a sample size would be required

A sample of 16577 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the z-score that has a p-value of .

The margin of error is of:

99% confidence level

So , z is the value of Z that has a p-value of , so .

She wants to estimate the proportion using a 99% confidence interval with a margin of error of at most 0.01. How large a sample size would be required?

We have no estimation for the proportion, and thus we use , which is when the largest sample size will be needed.

The sample size is n for which M = 0.01. So

Rounding up:

A sample of 16577 is required.

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step-by-step explanation: