According to an independent research, a point estimate of the proportion of U. S. consumers of black tea is p = 0.76. Calculate the sample size needed to be 95% confident that the error in estimating the true value of p is less than 0.015? Use the z-value rounded to two decimal places to obtain the answer. 4072.69

The sample size needed is 3115.

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:

Point estimate:

95% confidence level

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

Calculate the sample size needed to be 95% confident that the error in estimating the true value of p is less than 0.015?

This is n for which M = 0.015. So

Rounding up:

The sample size needed is 3115.

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