Question

Assume that you want to construct a 95% confidence interval estimate of a population mean. Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval. The sample standard deviation is given below. Margin of error equals=$66, standard deviation equals=$2222

The required sample size is _____. (Round up to the nearest whole number as needed.)

Answer 1

The estimated sample size is 4,354.

Explanation:

Hi, to solve this problem we have analyze the information given:

Confidence interval: 95%- it corresponds to a value of Z of 1.96

Margin of error (E) = $66

Standard deviation (σ) = $2222

To obtain the sample size, we have to apply the formula:

n = Z² σ² / E²

Replacing with the values given:

n= 1.96² 2222² / 66²

n= 4,354.24 ≅4,354

The estimated sample size is 4,354.

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